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Newly added pages can be seen from this page. Keep visiting to this page so that you will remain updated.en-usMathMon, 20 Jan 2020 14:09:25 -0500Mon, 20 Jan 2020 14:09:25 -0500math-only-math.comJan 20, Worksheet on Matrix | Solving Matrix Equations Worksheet | Answers
https://www.math-only-math.com/worksheet-on-matrix.htmlc892d4910b4d19c58e779f978a1810e3In Worksheet on matrix the questions are based on finding unknown elements and matrices from matrix equation. (i) Find the matrix C(B – A). (ii) Find A(B + C). (iii) Prove that A(B + C) = AB + AC. 2. Show that 6X – X^2 = 9I, where I is the unit matrix.Mon, 20 Jan 2020 14:09:22 -0500Jan 19, Worksheet on Matrix Multiplication |Multiplication of Matrices|Answers
https://www.math-only-math.com/worksheet-on-matrix-multiplication.html98859890a8336114acc7ad60337a8529Practice the questions given in the Worksheet on Matrix Multiplication. (i) Find AB and BA if possible. (ii) Verify if AB = BA. (iii) Find A^2. (iv) Find AB^2.Sun, 19 Jan 2020 14:18:12 -0500Jan 16, Problems on Classification of Matrices | Construct a Null Matrix
https://www.math-only-math.com/problems-on-classification-of-matrices.html98ba37058a7a3a0c288c58ba04c9c45aHere we will solve different types of Problems on classification of matrices. Indicate the class of each of the matrices. Construct a null matrix of the order 2 × 3 and a unit matrix of the order 3 × 3. Solution: A null matrix of the order 2 × 3 is Thu, 16 Jan 2020 12:55:47 -0500Jan 15, Matrix | Definition of a Matrix | Examples of a Matrix | Elements
https://www.math-only-math.com/matrix.htmla2b51f377bcbdb7b2376b213a01fe23eA rectangular array of mn elements aij into m rows and n columns, where the elements aij belongs to field F, is said to be a matrix of order m × n (or an m × n matrix) over the field F. Definition of a Matrix: A matrix is a rectangular arrangement or array of numbersWed, 15 Jan 2020 13:48:57 -0500Jan 15, Multiplication of Matrices | How to Multiply Matrices? |Rules|Examples
https://www.math-only-math.com/multiplication-of-matrices.html5ab21c7a924bc72b1dd4670be98eec63Two matrices A and B are said to be conformable for the product AB if the number of columns of A be equal to the number of rows of B. If A be an m × n matrix and B an n × p matrix then their product AB is defined to be the m × p matrix whose (ij)th element is obtained byWed, 15 Jan 2020 13:14:14 -0500Jan 15, Worksheet on Understanding Matrix | Possible Orders of the Matrix
https://www.math-only-math.com/worksheet-on-understanding-matrix.htmlb6f66a715f197bf1e3c7be7edf4e5b8fPractice the questions given in the Worksheet on understanding matrix. (i) What is the order of the matrix A? (ii) Find the (2, 1)th, (1, 2)th and (3, 2)th elements. (iii) Is it a rectangular matrix or a square matrix? 2. (i) A matrix has 4 elements. Write the possible orderWed, 15 Jan 2020 08:55:56 -0500Jan 13, Problems on Matrix Multiplication | Multiply Two Matrices
https://www.math-only-math.com/problems-on-matrix-multiplication.htmle38801bcc6526676dc0178229baf8eb2Here we will solve different types of Problems on Matrix Multiplication.write down the matrix AB. Would it be possible to find the product of BA? If so, compute it, and if not, give reasons.Mon, 13 Jan 2020 13:37:48 -0500Jan 8, Problems on Understanding Matrices | Order of a Matrix | Position of
https://www.math-only-math.com/problems-on-understanding-matrices.html0d5bb70879960380432d8677d25e6948Here we will solve different types of Problems on understanding matrices. (i) What is the order of the matrix A? (ii) Find (2, 1)th and (1, 2)th elements. Solution: (i) The order is 2 × 2 because there are 2 rows and 2 columns in the matrix (ii) (2, 1)th element = the numberWed, 8 Jan 2020 10:32:42 -0500Jan 7, Subtraction of Two Matrices | Matrix Subtraction | Subtract Matrices
https://www.math-only-math.com/subtraction-of-two-matrices.html0f383678ab617c720dd3181e2560b542We will learn how to find the subtraction of two matrices. If A and B two matrices of the same order then A – B is a matrix which is the addition of A and –B. The elements of A – B can also be obtained by subtracting the elements of B from the corresponding elements of A.Tue, 7 Jan 2020 13:31:01 -0500Jan 6, Negative of a Matrix | Solved Examples on Negative of a Matrix
https://www.math-only-math.com/negative-of-a-matrix.htmlf48c964c3e2bc2275ad677c2e6a9863bWe will discuss about Negative of a Matrix. The negative of the matrix A is the matrix (-1)A, written as – A. Clearly, the negative matrix is obtained by changing the signs of each element. Solved examples on Negative of a Matrix:Mon, 6 Jan 2020 13:39:48 -0500Jan 3, Multiplication of Two Matrices | Finding the Product of Two Matrices
https://www.math-only-math.com/multiplication-of-two-matrices.html9ef1c8f576d522cd776dd18593bc1ebeHere we will learn the process of Multiplication of two matrices. Two matrices A and B are conformable (compatible) for multiplication (i) AB if the number of columns in A = the number of rows in B (ii) BA if the number of columns in B = the number of rows in A. To find theFri, 3 Jan 2020 15:56:47 -0500Jan 2, Multiplication of a Matrix by a Number |Scalar Multiplication|Examples
https://www.math-only-math.com/multiplication-of-a-matrix-by-a-number.html7d4a891029709a601449b71467218fc0We will discuss here about the process of Multiplication of a matrix by a number. The multiplication of a matrix A by a number k gives a matrix of the same order as A, in which all the elements are k times the elements of A.Thu, 2 Jan 2020 15:09:24 -0500Jan 1, Addition of Two Matrices | Matrix Addition | Sum of Two Matrices
https://www.math-only-math.com/addition-of-two-matrices.html68477ca94e4ebd6239d20b0184651461We will learn how to find the addition of two matrices. Two matrices A and B are conformable (compatible) for addition if A and B are of the same order. The sum of A and B is a matrix of the same order and the elements of the matrix A + are obtained by adding theWed, 1 Jan 2020 16:12:33 -0500Dec 30, Classification of Matrices | Row Matrix | Column Matrix | Null Matrix
https://www.math-only-math.com/classification-of-matrices.html833f5fe395ec56626286cda8b150126cMatrices are classified according to the number of rows and columns, and the specific elements therein. (i) Row matrix: A matrix which has exactly one row is called a row matrix. For example, [45 -8], [8 9 10] are row matrices because each has only one row.Mon, 30 Dec 2019 15:59:29 -0500Dec 28, Definition of Equal Matrices | Examples of Equal Matrices
https://www.math-only-math.com/equal-matrices.html22c25f427e3f52494a6e4a87ada3bbc1Equality of two matrix: Two matrices [aij] and [bij] are said to be equal when they have the same number of rows and columns and aij = bij for all admissible values of i and j. Definition of Equal Matrices: Two matrices A and B are said to be equal if A and B have the sameSat, 28 Dec 2019 16:19:39 -0500Dec 27, Position of an Element in a Matrix | 10th Grade Matrix | Examples
https://www.math-only-math.com/position-of-an-element-in-a-matrix.html9ee0c3b323062d8967301c9766b5f6dcWe will learn how to find the position of an element in a matrix? 1. Consider the matrixHere, the element 5 falls on row number 1 and column 1. We say, 5 is the (1, 1)th element. Similarly, (1, 2)th element = -6 (2, 1)th element = 1 (2, 2)th element = 7 (3, 1)th element Fri, 27 Dec 2019 15:08:40 -0500Dec 26, Order of a Matrix | Determine the Order of Matrix | Solved Examples
https://www.math-only-math.com/order-of-a-matrix.html644ea49ff81a3dbbca64ffbe5e41e3b5How to determine the order of matrix? If a matrix has m rows and n columns, its order is said to be m × n (read as ‘m by n’). a matrix of the order m × n has mn elements. Hence, if the number of elements in a matrix be prime, it must have one row or one column.Thu, 26 Dec 2019 15:56:23 -0500Dec 25, nth Root of a | Meaning of \(\sqrt[n]{a}\) | Solved Examples
https://www.math-only-math.com/nth-root-of-a.html9a87f0467150c2e19e654feb167d6381We will discuss here about the meaning of \(\sqrt[n]{a}\). The expression \(\sqrt[n]{a}\) means ‘nth rrot of a’. So, (\(\sqrt[n]{a}\))^n = a. Also, (a^1/a)^n = a^n*1/n = a^1 = a. So, \(\sqrt[n]{a}\) = a^1/n. Examples: \(\sqrt[3]{8}\) = 8^1/3 = (2^3)^1/3 = 2^3 * 1/3 = 2^1Wed, 25 Dec 2019 15:11:46 -0500Dec 22, The laws of exponents are explained here along with their examples.
https://www.math-only-math.com/laws-of-exponents.html02f2a1d7a07a3e07df708e8c06129b5cThe laws of exponents are explained here along with their examples. In multiplication of exponents if the bases are same then we need to add the exponents.Sun, 22 Dec 2019 15:56:28 -0500Dec 22, Laws of Indices | Laws of Exponents| Rules of Indices |Solved Examples
https://www.math-only-math.com/laws-of-indices.htmlef4c97a8fc9becaae447002b991aff1bWe will discuss here about the different Laws of Indices. If a, b are real numbers (>0, ≠ 1) and m, n are real numbers, following properties hold true. (i) am × an = am + n (ii) a-m = \(\frac{1}{a^{m}}\) (iii) \(\frac{a^{m}}{a^{n}}\) = am – n = \(\frac{1}{a^{m - n}}\) Sun, 22 Dec 2019 15:40:55 -0500Dec 20, Power of a Number | Exponent | Index | Negative Exponents | Examples
https://www.math-only-math.com/power-of-a-number.htmlec54bb3573c9947f69fa8b0b4ca8d92cHere we will learn the Power of a Number. We know a × a = a^2, a × a × a = a^3, etc., and a × a × a × ... n times = a^n, where n is a positive integer. a^n is a power of a whose base is a and the index of power is n. a^p/q is the qth root of a^p if p, q are positive integersFri, 20 Dec 2019 14:00:33 -0500Dec 19, Worksheet on Factorization | Hints | Miscellaneous Factorization
https://www.math-only-math.com/Worksheet-on-Factorization.htmlf38c07077c6332e013dc81cbead2b5a5Practice the questions given in the Worksheet on Factorization. Factorization of expressions of the form a^3 ± b^3 1. Factorize: (i) 8x^3 + 27y^3 (ii) 216a^3 + 1 (iii) a^6 + 1 (iv) x^3 + \(\frac{1}{x^{3}}\) (v) a^3 + 8b^6Thu, 19 Dec 2019 12:59:55 -0500Dec 9, Factorization of expressions of the Form a^3 + b^3 + c^3 – 3abc
https://www.math-only-math.com/factorization-of--expressions-of-the-form-a-cube-plus-b-cube-plus-c-cube-minus-3abc.html90cf66f59a98dffa1d646ece2b2afbedHere we will learn the process of On Factorizations of expressions of the Form a^3 + b^3 + c^3 – 3abc. We have, a^3 + b^3 + c^3 – 3abc = (a + b + c)(a^2 + b^2 + c^2 – bc – ca – ab). [Verify by actual multiplication.] Example: Factorize: x^3 + y^3 – 3xy + 1. Solution: HereMon, 9 Dec 2019 13:00:28 -0500Dec 9, Factorization of Expressions of the Form a^3 + b^3 + c^3, a + b + c=0
https://www.math-only-math.com/factorization-of-expressions-of-the-form-a-cube-plus-b-cube-plus-c-cube.html127b37b29670a1231cbeed6f8edf6be3Here we will learn the process of On Factorization of expressions of the Form a^3 + b^3 + c^3 , where a + b + c = 0. We have, a^3 + b^3 + c^3 = a^3 + b^3 – (-c)^3 = a^3 + b^3 – (a + b)^3, [Since, a + b + c = 0] = a^3 + b^3 – {a^3 + b^3 + 3ab(a + b)} = -3ab(a + b) = -3ab(-cMon, 9 Dec 2019 12:49:59 -0500Dec 9, Miscellaneous Problems on Factorization | Application Problems
https://www.math-only-math.com/miscellaneous-problems-on-factorization.html54cffd60de675f72071defa110bcab76Here we will solve different types of Miscellaneous Problems on Factorization. 1. Factorize: x(2x + 5) – 3 Solution: Given expression = x(2x + 5) – 3 = 2x^2 + 5x – 3 = 2x^2 + 6x – x – 3, [Since, 2(-3) = - 6 = 6 × (-1), and 6 + (-1) = 5] = 2x(x + 3) – 1(x + 3)Mon, 9 Dec 2019 12:38:53 -0500Nov 24, Factorization of Expressions of the Form a^3 - b^3 | Solved Examples
https://www.math-only-math.com/factorization-of-expressions-of-the-form-a-cube-minus-b-cube.html0fb19ef636a9c0a28b9d0e5dcb4be177Here we will learn the process of Factorization of Expressions of the Form a^3 - b^3. We know that (a - b)^3 = a^3 - b^3 - 3ab(a - b), and so a^3 - b^3 = (a - b)^3 + 3ab(a - b) = (a - b){(a - b)^2 + 3ab} Therefore, a^3 - b^3 = (a - b)(a^2 + ab + b^2) Example: 1. Factorize:Sun, 24 Nov 2019 11:06:29 -0500Nov 24, Factorization of Expressions of the Form a^3 + b^3 | Solved Examples
https://www.math-only-math.com/factorization-of-expressions-of-the-form-a-cube-plus-b-cube.htmla42ffad5bcf2c556c67a3177acd9a85aHere we will learn the process of Factorization of Expressions of the Form a^3 + b^3. We know that (a + b)^3 = a^3 + b^3 + 3ab(a + b), and so a^3 + b^3 = (a + b)^3 – 3ab(a + b) = (a + b){(a + b)^2 – 3ab} Therefore, a^3 + b^3 = (a + b)(a^2 – ab + b^2). Example: 1. Factorize:Sun, 24 Nov 2019 10:52:36 -0500Nov 23, Worksheet on Factorization of the Trinomial ax^2 + bx + c | Answers
https://www.math-only-math.com/worksheet-on-factorization-of-the-trinomial-ax-square-plus-bx-plus-c.html1b16a9412ab882790032cd86fbbc52f4Practice the questions given in the worksheet on factorization of the trinomial ax^2 + bx + c. 1. Factorization of a perfect-square trinomial. (i) a^2 + 6a + 9 (ii) a^2 + a + \(\frac{1}{4}\) (iii) 25x^2 – 10x + 1 (iv) 4x^2 – 4xy + y^2 2. Factorization of expressions of theSat, 23 Nov 2019 14:31:18 -0500Nov 18, Problems on Factorization of Expressions of the Form x^2 +(a + b)x +ab
https://www.math-only-math.com/problems-on-factorization-of-expressions-of-the-form-ax-square-plus-bx-plus-c.html52ef5c4880c0d3668031380c8abe9ac4Here we will solve different types of Problems on Factorization of Expressions of the Form x^2 + (a + b)x + ab. 1. Factorize: a^2 + 25a - 54 Solution: Here, constant term = -54 = (27) × (-2), and 27 + (-2) = 25 (= coefficient of a). Therefore, a^2 + 25a – 54Mon, 18 Nov 2019 13:51:37 -0500Nov 17, Factorization of Expressions of the Form ax^2 + bx + c, a ≠ 1|Examples
https://www.math-only-math.com/factorization-of-expressions-of-the-form-ax-square-plus-bx-plus-c.htmlf223af9f9b881f4d62425eb511376a4aThe below examples show that the method of factorizing ax^2 + bx + c by breaking the middle term involves the following steps. Steps: 1.Take the product of the constant term and the coefficient of x^2, i.e., ac. 2. Break ac into two factors p, q whose sum is b,Sun, 17 Nov 2019 13:49:20 -0500Nov 13, Factorization of Expressions of the Form x^2 + (a + b)x + ab |Examples
https://www.math-only-math.com/factorization-of-expressions-of-the-form-x-square-plus-sum-of-a-plus-b-times-x-plus-a-times-b.html14b60cc9e9671950d97dd82aa69a460aHere we will learn the process of Factorization of Expressions of the Form x^2 + (a + b)x + ab. We know, (x + a)(x + b) = x^2 + (a + b)x + ab. Therefore, x^2 + (a + b)x + ab = (x + a)(x + b). 1. Factorize: a^2 + 7a + 12. Solution: Here, constant term = 12 = 3 × 4, and 3 + 4Wed, 13 Nov 2019 09:52:29 -0500Nov 10, Factorization of a Perfect-square Trinomial | Solved Examples
https://www.math-only-math.com/factorization-of-a-perfect-square-trinomial.html48890bf9ac661b367380b99213c79577Here we will learn the process of Factorization of a Perfect-square Trinomial. A trinomial of the form a^2 ± 2ab + b^2 = (a ± b)^2 = (a ± b)(a ± b) Solved examples on Factorization of a Perfect-square Trinomial 1. Factorize: x^2 + 6x + 9 Solution: Here, given expressionSun, 10 Nov 2019 13:12:44 -0500Nov 4, Problems on Factorization Using a^2 – b^2 = (a + b)(a – b)
https://www.math-only-math.com/problems-on-factorization-using-a-square-minus-b-square.html8a59984ada7331124d57659e85003826Problems on Factorization using a^2 – b^2 = (a + b)(a – b) Here we will solve different types of Problems on Factorization using a^2 – b^2 = (a + b)(a – b). 1. Factorize: 4a^2 – b^2 + 2a + b Solution: Given expression = 4a^2 – b^2 + 2a + b = (4a^2 – b^2) + 2a + bMon, 4 Nov 2019 14:04:42 -0500Nov 2, Problems on Factorization of Expressions of the Form a^2 – b^2
https://www.math-only-math.com/problems-on-factorization-of-expressions-of-the-form-a-square-minus-b-square.html1da0069d0fa9ba719bd72fca8ebce9a4Here we will solve different types of Problems on Factorization of expressions of the form a^2 – b^2. 1. Resolve into factors: 49a^2 – 81b^2 Solution: Given expression = 49a^2 – 81b^2 = (7a)^2 – (9b)^2 = (7a + 9b)(7a – 9b). 2.Factorize: (x + y)^2 – 4(x - y)^2 Solution: GivenSat, 2 Nov 2019 15:17:28 -0400Nov 1, Problems on Factorization by Grouping of Terms | Find the Factors
https://www.math-only-math.com/problems-on-factorization-by-grouping-of-terms.html58b0925cbd73933595bfd525bb311482Here we will solve different types of Problems on Factorization by grouping of terms. 1. Factorize: a^2 – (b – 5)a – 5b. Solution: Given expression = a^2 – (b – 5)a – 5b = a^2 – ba + 5a – 5b = a(a - b) + 5(a - b) = (a – b)(a + 5). 2. Factorize: a^2 + b^2 + a + b + 2abFri, 1 Nov 2019 14:53:22 -0400Oct 31, Introduction to Factorization | Different of Two Squares | Examples
https://www.math-only-math.com/introduction-to-factorization.html36e9e8be9928b1fa1c56e66a1672d53bWe will discuss here about the introduction to factorization. The method of expressing a given polynomial as a product of two or more polynomials is called factorization. The polynomials whose product is the given polynomial are called its factors. You are already familiarThu, 31 Oct 2019 14:09:58 -0400Oct 25, Problems on Expanding of (a ± b)\(^{3}\) and its Corollaries |Examples
https://www.math-only-math.com/problems-on-expansion-of-a-plus-minus-b-whole-cube-and-its-corollaries.html7a82e6578ca9cb4da42f220edf5f5110Here we will solve different types of application problems on expanding of (a ± b)\(^{3}\) and its corollaries. 1. Expanding the following: (i) (1 + x)\(^{3}\) (ii) (2a – 3b)\(^{3}\) (iii) (x + \(\frac{1}{x}\))\(^{3}\) Solution: (i) (1 + x)\(^{3}\) = 1\(^{3}\) +Fri, 25 Oct 2019 18:02:47 -0400Oct 22, Worksheet on Application Problems on Expansion of Powers of Binomials
https://www.math-only-math.com/worksheet-on-application-problems-on-expansion-of-powers-of-binomials-and-trinomials.html21d7f54c3e6359bc86902df6d709caa2Practice the questions given in the worksheet on application problems on expansion of powers of binomials and trinomials. 1. Use (a ± b)^2 = a^2 ± 2ab + b2 to evaluate the following: (i) (3.001)^2 (ii) (5.99)^2 (iii) 1001 × 999 (iv) 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37Tue, 22 Oct 2019 11:38:36 -0400Oct 22, Application Problems on Expansion of Powers of Binomials & Trinomials
https://www.math-only-math.com/application-problems-on-expansion-of-powers-of-binomials-and-trinomials.htmlde09bec634791c1c307f991f118e9eaaHere we will solve different types of application problems on expansion of powers of binomials and trinomials. 1. Use (x ± y)^2 = x^2 ± 2xy + y^2 to evaluate (2.05)^2. Solution: (2.05)^2 = (2 + 0.05)^2 = 2^2 + 2 × 2 × 0.05 + (0.05)^2 = 4 + 0.20 + 0.0025 = 4.2025.Tue, 22 Oct 2019 11:30:44 -0400Oct 21, Expansion of (x + a)(x + b)(x + c) | Solved Examples | Problems | Hint
https://www.math-only-math.com/expansion-of-x-plus-a-times-x-plus-b-times-x-plus-c.html72f2294e1523dd5870b712a506e4fda8We will discuss here about the expansion of (x + a)(x + b)(x + c). (x + a)(x + b)(x + c) = (x + a){(x + b)(x + c)} = (x + a){x\(^{2}\) + (b + c)x + bc} = x{x\(^{2}\) + (b + c)x + bc} + a{x\(^{2}\) + (b + c)x + bc} = x\(^{3}\) + (b + c)x\(^{2}\) + bcx + ax\(^{2}\) + a(b + c)xMon, 21 Oct 2019 13:13:08 -0400Oct 20, Simplification of (a + b + c)(a\(^{2}\)+b\(^{2}\)+c\(^{2}\)–ab–bc– ca)
https://www.math-only-math.com/simplification-of-a-cube-plus-b-cube-plus-c-cube-minus-three-abc.html2b68a2ce4c6e5f303265f70c1721d2bcWe will discuss here about the expansion of (a + b + c)(a\(^{2}\) + b\(^{2}\) + c\(^{2}\) – ab – bc – ca). (a + b + c)(a\(^{2}\) + b\(^{2}\) + c\(^{2}\) – ab – bc – ca) = a(a\(^{2}\) + b\(^{2}\) + c\(^{2}\) – ab – bc – ca) + b(a\(^{2}\) + b\(^{2}\) + c\(^{2}\) –ab – bc – ca)Sun, 20 Oct 2019 11:37:12 -0400Oct 17, Simplification of (a ± b)(a^2 ∓ ab + b^2) | Sum or Difference of Cubes
https://www.math-only-math.com/simplification-of-a-cube-plus-minus-b-cube.html525b25cc2dc1d18243ccbb623e59a90fWe will discuss here about the expansion of (a ± b)(a\(^{2}\) ∓ ab + b\(^{2}\)). (a + b)(a\(^{2}\) - ab + b\(^{2}\)) = a(a\(^{2}\) - ab + b\(^{2}\)) + b(a\(^{2}\) - ab + b\(^{2}\)) = a\(^{3}\) - a\(^{2}\)b + ab\(^{2}\) + ba\(^{2}\) - ab\(^{2}\) + b\(^{3}\) =Thu, 17 Oct 2019 12:17:46 -0400Oct 15, Expansion of (a ± b)\(^{3}\) | Algebraic Expressions and Formulas
https://www.math-only-math.com/expansion-of-a-plus-minus-b-whole-cube.html50dd2e004723f6e82f18b50203e5ee4fWe will discuss here about the expansion of (a ± b)\(^{3}\). (a + b)\(^{3}\) = (a + b) ∙ (a + b)\(^{2}\) = (a + b)(a\(^{2}\) + 2ab + b\(^{2}\)) = a(a\(^{2}\) + 2ab + b\(^{2}\)) + b(a\(^{2}\) + 2ab + b\(^{2}\))=a\(^{3}\)+2a\(^{2}\)b+ab\(^{2}\)+ba\(^{2}\)+2ab\(^{2}\)+b\(^{3}\)Tue, 15 Oct 2019 11:49:46 -0400Oct 14, Express a^2 + b^2 + c^2 – ab – bc – ca as Sum of Squares
https://www.math-only-math.com/express-as-sum-of-squares.html1f589af3cf1952bdc53ae88223b19e67Here we will express a^2 + b^2 + c^2 – ab – bc – ca as sum of squares. If a, b, c are real numbers then (a – b)^2, (b – c)^2 and (c – a)^2 are positive as square of every real number is positive. So, a^2 + b^2 + c^2 – ab – bc – ca is always positive.Mon, 14 Oct 2019 14:07:43 -0400Oct 11, Worksheet on Simplification of (a + b)(a – b) | Hint | Answers
https://www.math-only-math.com/worksheet-on-simplification-of-the-product-of-a-plus-b-and-a-minus-b.html4201253dd23654fab680fb63accf0d25Practice the questions given in the worksheet on simplification of (a + b)(a – b). 1. Simplify by applying standard formula. (i) (5x – 9)(5x + 9) (ii) (2x + 3y)(2x – 3y) (iii) (a + b – c)(a – b + c) (iv) (x + y – 3)(x + y + 3) (v) (1 + a)(1 – a)(1 + a^2)Fri, 11 Oct 2019 17:17:00 -0400Oct 10, Worksheet on Completing Square |Find the Missing Term| Perfect Squares
https://www.math-only-math.com/worksheet-on-completing-a-square.html388ee09538142e6b0d041bf825e94462Practice the questions given in the worksheet on completing square. Write the following as a perfect square. (i) 4X^2 + 4X + 1 (ii) 9a^2 – 12ab + 4b^2 (iii) 1 + 6/a + 9/a^2 2. Indicate the perfect squares among the following. Express each of the perfect squares as the squareThu, 10 Oct 2019 12:56:07 -0400Oct 10, Completing a Square | Solved Examples on Completing a Square
https://www.math-only-math.com/completing-a-square.htmlc2d566000272f00680a11a39f5ccae3bHere we will learn how to completing a square.Problems on completing a square 1. What should be added to the polynomial 4m^2 + 8m so that it becomes perfect square? Solution: 4m^2 + 8m = (2m)^2 + 2 ∙ (2m) ∙ 2Thu, 10 Oct 2019 12:22:16 -0400Oct 9, Worksheet on Expansion of (x ± a)(x ± b) | Find the Product | Answers
https://www.math-only-math.com/worksheet-on-expansion-of-the-product-of-x-plus-minus-a-and-x-plus-minus-b.html00349c09970702c3a5245b092cbb2f21Practice the questions given in the worksheet on expansion of (x ± a)(x ± b). 1. (i) Find the product using standard formula. (i) (x + 2)(x + 5) (ii) (a – 4)(a – 7) (iii) (x + 1)(x – 8) (iv) (a – 3)(a + 2) (v) (3x + 1)(3x + 2) (vi) (4x – y)(4x + 2y) 2. Find the product.Wed, 9 Oct 2019 15:32:17 -0400Oct 1, Worksheet on Expanding of (a ± b ± c)^2 and its Corollaries | Answers
https://www.math-only-math.com/worksheet-on-expansion-of-a-plus-minus-b-plus-minus-c-whole-square-and-its-corollaries.html10839011dd64723ae2a3fac3d32c54b8Practice the questions given in the worksheet on expanding of (a ± b ± c)^2 and its corollaries. 1. Expand the squares of the following trinomials. (i) a + 2b + 3c (ii) 2x + 3y + 4z (iii) x + 2y – 3z (iv) 3a – 4b – c (v) 1 – x - \(\frac{1}{x}\) (vi) 1 – a – a^2. 2. Simplify:Tue, 1 Oct 2019 11:24:15 -0400Sep 30, Worksheet on Expansion of (a ± b)^2 and its Corollaries | Answers
https://www.math-only-math.com/worksheet-on-expansion-of-a-plus-minus-b-whole-square-and-its-corollaries.htmla63c032991f36d3f971d8cae44cefff8Practice the questions given in the worksheet on expansion of (a ± b)^2 and its corollaries. 1. Expand the squares of the following: (i) 4x + y (ii) 5a + 3b (iii) 2x + \(\frac{1}{x}\) 2. Expand the following: (i) (x – 2y)^2 (ii) (3y – 2z)^2 (iii) (3x - \(\frac{1}{3x}\))^2Mon, 30 Sep 2019 18:40:36 -0400Sep 23, Simplification of (a + b)(a – b) | | Solved Examples on Simplification
https://www.math-only-math.com/simplification-of-the-product-of-a-plus-b-and-a-minus-b.html4107bee1e909ea2b94f6bff45837090fWe will discuss here about the Simplification of (a + b)(a – b). (a + b)(a – b) = a(a – b) + b(a – b) = a\(^{2}\) - ab + ba - b\(^{2}\) = a\(^{2}\) - b\(^{2}\) Thus, we have (a + b)(a - b) = a\(^{2}\) - b\(^{2}\) Solved Examples on Simplification of (a + b)(a – b) 1.Mon, 23 Sep 2019 10:19:44 -0400Sep 22, Expansion of (x ± a)(x ± b) | Special Identities | Expanding Binomials
https://www.math-only-math.com/expansion-of-the-product-of-x-plus-minus-a-and-x-plus-minus-b.htmlf35606e89057f8ca4efdf559232b995eWe will discuss here about the expansion of (x ± a)(x ± b) (x + a)(x + b) = x(x + b) + a (x + b) = x^2 + xb + ax + ab = x^2 + (b + a)x + ab (x - a)(x - b) = x(x - b) - a (x - b) = x^2 - xb - ax + ab = x^2 - (b + a)x + ab (x + a)(x - b) = x(x - b) + a (x - b) = x^2 - xb Sun, 22 Sep 2019 13:58:25 -0400Sep 22, Expansion of (a ± b ± c)^2 | Square of a Trinomial | Algebra Formulas
https://www.math-only-math.com/expansion-of-a-plus-minus-b-plus-minus-c-whole-square.html08c7c163459f15be3f817c2fb0d96ed0We will discuss here about the expansion of (a ± b ± c)^2. (a + b + c)^2 = {a + (b + c)}^2 = a^2 + 2a(b + c) + (b + c)^2 = a^2 + 2ab + 2ac + b^2 + 2bc + c^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) = sum of squares of a, b, c + 2(sum of the products of a, b, c taking two at a tiSun, 22 Sep 2019 11:02:52 -0400Sep 21, A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles
https://www.math-only-math.com/a-rhombus-is-a-parallelogram-whose-diagonals-meet-at-right-angles.htmle62cfb3b5b2d921b3380bbd941894ca6Here we will prove that a rhombus is a parallelogram whose diagonals meet at right angles. Given: PQRS is a rhombus. So, by definition, PQ = QR = RD = SP. Its diagonals PR and QS intersect at O. To prove: (i) PQRS is a parallelogram. (ii) ∠POQ = ∠QOR = ∠ROS = ∠SOP = 90°.Sat, 21 Sep 2019 17:34:35 -0400Sep 21, Pair of Opposite Sides of a Parallelogram are Equal and Parallel
https://www.math-only-math.com/pair-of-opposite-sides-of-a-parallelogram-are-equal-and-parallel.html8f16ce62bfe73e65784fa3a855a68d5bHere we will discuss about one of the important geometrical property of parallelogram. A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel Given: PQRS is a quadrilateral in which PQ = SR and PQ ∥ SR. To prove: PQRS is a parallelogram.Sat, 21 Sep 2019 17:20:41 -0400Sep 21, A Quadrilateral is a Parallelogram if its Diagonals Bisect each Other
https://www.math-only-math.com/a-quadrilateral-is-a-parallelogram-if-its-diagonals-bisect-each-other.html135e7b7c04ff496035756b1d3770af54Here we will discuss about a quadrilateral is a parallelogram if its diagonals bisect each other. Given: PQRS is a quadrilateral whose diagonals PR and QS bisect each other at O, i.e., OP = OR and OQ = OS. To prove: PQRS is a parallelogram. Proof: In ∆OPQ and ∆ORS, OP = ORSat, 21 Sep 2019 16:49:01 -0400Sep 21, Diagonals of a Parallelogram Bisect each Other | Diagonals Bisect each
https://www.math-only-math.com/diagonals-of-a-parallelogram-bisect-each-other.html9cbbc2ced76b29141b62d992d0005cd9Here we will discuss about the diagonals of a parallelogram bisect each other. In a parallelogram, diagonals bisect each other and each diagonal bisects the parallelogram into two congruent triangles. Given: PQRS is a parallelogram in which PQ ∥ SR and PS ∥ QR. Its diagonalsSat, 21 Sep 2019 15:27:35 -0400Sep 20, Expansion of (a ± b)^2 | Power of the Trinomial | Algebraic Expression
https://www.math-only-math.com/expansion-of-a-plus-minus-b-whole-square.html37ca8e866688946927f0b48a9f8ee399A binomial is an algebraic expression which has exactly two terms, for example, a ± b. Its power is indicated by a superscript. For example, (a ± b)2 is a power of the binomial a ± b, the index being 2. A trinomial is an algebraic expression which has exactly three termsFri, 20 Sep 2019 18:47:33 -0400Sep 18, Opposite Angles of a Parallelogram are Equal | Related Solved Examples
https://www.math-only-math.com/opposite-angles-of-a-parallelogram-are-equal.htmld514b8b7a64661180d3d25c39285acb0Here we will discuss about the opposite angles of a parallelogram are equal. In a parallelogram, each pair of opposite angles are equal. Given: PQRS is a parallelogram in which PQ ∥ SR and QR ∥ PS To prove: ∠P = ∠R and ∠Q = ∠S Construction: Join PR and QS. Proof: Statement:Wed, 18 Sep 2019 18:16:50 -0400Sep 18, Opposite Sides of a Parallelogram are Equal | Solved Examples
https://www.math-only-math.com/opposite-sides-of-a-parallelogram-are-equal.html677aa4b6b32c8665a0f3fefd9b42a7cdHere we will discuss about the opposite sides of a parallelogram are equal in length. In a parallelogram, each pair of opposite sides are of equal length. Given: PQRS is a parallelogram in which PQ ∥ SR and QR ∥ PS. To prove: PQ = SR and PS = QR. Construction: Join PRWed, 18 Sep 2019 17:30:25 -0400