Square of The Sum of Two Binomials
How to find the square of the sum of two binomials?
(a + b) (a + b) = a(a + b) + b(a + b)
= a2 + ab + ba + b2
= a2 + 2ab + b2
= a2 + b2+ 2ab
Therefore, (a + b)2 = a2 + b2 + 2ab
Square of the sum of two terms = square of 1st term + square of 2nd term + 2 × fist term × second term
This is called the binomial square.
It is stated as: the Square of the binomial (sum of two unlike term) is the square of the first term plus the square of the second term plus twice the product of two terms.
Worked-out examples on square of the sum of two binomials:
Solution:
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 2x and b = 3y
= (2x)2 + (3y)2 + 2 (2x) (3y)
= 4x2 + 9y2 + 12xy
Therefore, (2x + 3y)2 = 4x2 + 9y2 + 12xy.
2. Evaluate 1052 using the formula of (a + b)2.
Solution:
1052 = (100 + 5)2
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 100 and b = 5
(100 + 5)2
= (100)2 + (5)2 + 2 (100) (5)
= 10000 + 25 + 1000
= 11025
Therefore, 1052 = 11025.
3. Evaluate (10.1)2 using the identity.
Solution:
(10.1)2 = (10 + 0.1)2
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 10 and b = 0.1
(10 + 0.1)2
= (10)2 + (0.1)2 + 2 (10) (0.1)
= 100 + 0.01 + 2
= 102.01
Therefore, (10.1)2 = 102.01.
4. Use the formula of square of the sum of two terms to find the product of (1/5 x + 3/2 y) (1/5 x + 3/2 y).
Solution:
(1/5 x + 3/2 y) (1/5 x + 3/2 y) = (1/5 x + 3/2 y)2
We know that (a + b)2 = a2 + b2 + 2ab
Here, a = 1/5 x and b = 3/2 y
= (1/5 x)2 + (3/2 y)2 +
= 1/25 x2 + 9/4 y2 + 3/5 xy
Therefore, (1/5 x + 3/2 y) (1/5 x + 3/2 y) = 1/25 x2 + 9/4 y2 + 3/5 xy.
From the above solved problems we come to know square of a number means multiplying a number with itself, similarly, square of the sum of two binomial means multiplying the binomial with itself.
7th Grade Math Problems
8th Grade Math Practice
From Square of The Sum of Two Binomials to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Dividing 3-Digit by 1-Digit Number | Long Division |Worksheet Answer
Apr 24, 24 03:46 PM
Dividing 3-Digit by 1-Digit Numbers are discussed here step-by-step. How to divide 3-digit numbers by single-digit numbers? Let us follow the examples to learn to divide 3-digit number by one-digit nu… -
Symmetrical Shapes | One, Two, Three, Four & Many-line Symmetry
Apr 24, 24 03:45 PM
Symmetrical shapes are discussed here in this topic. Any object or shape which can be cut in two equal halves in such a way that both the parts are exactly the same is called symmetrical. The line whi… -
Mental Math on Geometrical Shapes | Geometry Worksheets| Answer
Apr 24, 24 03:35 PM
In mental math on geometrical shapes we will solve different type of problems on simple closed curves, polygons, basic geometrical concepts, perpendicular lines, parallel lines, circle, terms relates… -
Circle Math | Terms Related to the Circle | Symbol of Circle O | Math
Apr 24, 24 02:57 PM
In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We… -
Fundamental Geometrical Concepts | Point | Line | Properties of Lines
Apr 24, 24 12:38 PM
The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples.