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Algebraic ExpressionWhat is an algebraic expression?The combination of constants and variables, connected by signs of fundamental operations (+, , ×, ÷) is called an algebraic expression. 2x – 3y + 9z is an algebraic expression. In the algebraic expression 3x^{2} + 7y^{3}  4xy. 3x^{2}, 7y^{3}, 4xy are called terms of the expression. Classification of algebraic expressionsMonomial: An algebraic expression containing only one term is called a monomial.For example; 3x, 7, ^{5}/_{9} a^{2}bc are all monomials. Binomial: An algebraic expression containing two terms is called a binomial. For example; x – 7, 5x + 9y, ab + care all binomials. Trinomial: An algebraic expression containing three terms is called a trinomial. For example; x – y + 7, 3x + 4y – 5z, a^{3} + b^{2} + c^{4} are all trinomials. Multinomial: An algebraic expression containing two term is called a multinomial. For example; x^{3} y^{2} + 2x^{2}y – 3xy + 7, a^{2} + b^{2}  4c^{2}  d^{2}, l + m + n – p are all multinomials. Polynomial: In an algebraic expression, if the power of variables is a nonnegative integer; then that expression is called a polynomial. For example; 3x^{2} + 4x + 7 is a polynomial. x^{2} + ^{3}/_{x} is not a polynomial. [The power of x in ^{3}/_{x} is negative. Therefore, ^{3}/_{x} = 3x^{1}] 5√x + 2x^{2}  5 is not a polynomial. [The power of x in 5√x is in fraction. Therefore, 5√x = 5x^{1/2}] A. Express the following algebraic expressions with the help of signs and symbols:● The sum of x and y.x + y ● The subtraction of n from m. m – n ● The product of a and b. ab ● x divided by 4. x/4 ● 4 divided by m. 4/m ● The sum of 5 and p. 5 + p ● The product of z and 15. 15 × z ● 5 less than 3 times x. 3x + 5 ● Half of the product of 4 and x. 4x/2 ● Onetenth of y. y/10 ● 6 less than the sum of x and y. (x + y) – 6 ● The values of a and b is equal. a = b ● The values of p is greater than of q. P > q ● 8 is less than y. 8 < y B. Express the following algebraic expressions in words:● p + qThe sum of p and q ● 5a 5 times of a ● x/6 1/6 the part of x. ● x + y + 1 The sum of x, y and 1 ● 2p + r The sum of r and two times of p ● m + 3x The sum of m and three times of x ● a – 3b Deduction of 3 times of b from a ● 3x – y Deduction of y from 3 times of x ● (a + 2b)/3 1/3 of sum of a and two times b ● p/3 + 5 Sum of 1/3 rd portion of p and 5 ● 9 > 2m 9 is greater than two times of m ● x + y < 10 Sum of x + y is less than 10 C. Express the following algebraic expressions using symbol if it is necessary.● Ben has $12, Kyle has $ x more. How many dollars does Kyle possess?12 + x ● You worked out x sums yesterday. Today you have worked out 10 sums less. How many sum have you worked out today? x – 10 ● A taxi driver had earned a dollar on a day and $6 less on the next day. How much money has he earned on the next day? a – 6 ● Tom has 5 exercise books. His father bought x more exercise books for her. How many exercise books now Tom have? 5 + x ● Ron had 15 marbles, he lost y marbles. How many marbles are now remaining with him? 15 – y ● Kelly is x years older than John. The present age of John is y years. How old is Kelly now? What will be their ages after 5 years? Kelly = y + x, John = y + 5, Kelly = y + x + 5 ● A labourer earns $x daily. How much will he earn in 7 days? 7x ● There are x rows of trees in Harry’s garden. In each row there are 10 trees. How many trees are there in the garden? 10x ● You have two exercise books. Your father gave you some more exercise books? How many exercise books are there with you now? 2 + x ● Roby had 7 color pencils. He has lost some of them. How many color pencils he has now? 7 – x ● Shelly’s age is 13 years. (i) What was her age x years before? (ii) What will be her age y years hence? (i) (13 – x) years (ii) (13 + x) years ● Two less than one third of x x/3 – 2 ● One third of a a/3 ● Mike is 3 years older than his brother Rex. If Rex’s age is p years, what will be Mike’s age? (p + 3) years ● The price of a dozen of banana is $ x. What will be the price of 4 dozen of bananas? 4x ● The difference of two numbers is y, the greater number is 18. Find the smaller number. Smaller number = 18 – y ● The product of two numbers is 64. One of them is d. Find the other. Other number = 64/d ● Your age is 12 years now. What was your age p year ago? What will be your age after p years? Age before p years = (12 – y) years Age after p years = (12 + y) years ● Algebraic Expression ● Algebraic Expression ● Addition of Algebraic Expressions ● Subtraction of Algebraic Expressions ● Multiplication of Algebraic Expression ● Division of Algebraic Expressions 8th Grade Math Practice


