29. Algebraic Expression : Value, Addition, Subtraction, Multiplication & Division

 UNIT 7 : ALGEBRA

29 ALGEBRAIC EXPRESSION: VALUE, ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION

Learn and Remember :

1. Algebraic Expression : Using letters of English alphabet along wth numbers to form a

mathematical expression is known as algebraic expression. 5x; 2y – 3; 3m2 – 5mn + 6n2, etc. are algebraic expressions.

In 5x, 5 (the numeral) is called the coefficient, x (the letter) is called the variable. 2. Some terminology in Algebra : (1) Term : An algebraic expression with only multiplication or division as the operations

involved, is called 'term'.

(ii) Coefficient : A quantity multiplying a variable in an algebraic term is called the

coefficient of that variable. (1) 4 is the coefficient of x in the term 4x. (2) (-7) is the coefficient of m?n in the term – 7m’n.

(3) 1 is the coefficient of x in the term x. (iii) Monomial : An algebraic expression which has only one term in it is said to be a monomial.

e.g. 5x, – 6a2b3, 7, etc. are monomials.

(iv) Polynomials : An algebraic expression which has two or more than two terms in the

form of addition or subtraction (or both), are called polynomials.

(v) In particular, a polynomial with two terms is called a binomial and a polynomial with

three terms is called a trinomial.

(vi) A term in an algebraic expression, which is only a rational number, is called a

'constant term' or a 'constant'.

e.g. in the algebraic expression 5x2 + 6x + 7, 7 is the constant term. 3. Like Terms, Addition, Subtraction : Consider the terms 2xy?, 6xy?, – 5xy?. These

terms have only the coefficient of xy2 different. Such terms are called like terms. Like terms can be added or subtracted by adding or subtracting their coefficients. e.g. 2xy2 + 6xy? – 5xy2 = (2+ 6 – 5) xy2 = 3xy? Unlike terms cannot be added or subtracted by adding or subtracting their coefficients.

e.g. 2xy? and 3x’y are unlike terms the sum of these two terms is 2xyz + 3x2y (the coefficients 2 and 3 cannot be added). Horizontal or vertical arrangement of terms may be done for addition or subtraction.

4. Value of an algebraic expression: Consider the algebraic expression 5x? -- 2x + 3.

The value of the expression 5x? - 2x + 3 for x = 1 is obtained by replacing x by 1 i.e. 5(1)' - 2(1) + 3. = 5 - 2 + 3 = 6

Thus the value of 5x2 - 2x + 3 for x = 1 is 6. 5. Product of binomials : (1) (x + a)(x+b) = x + ( a +b)x + ab e.g. 

(1) (x+3)(x+5) = x + (3+5)x +3 5 = **+ 8x + 15 (2) (x - 7)(x + 3) = x° +13 + - 7)]x + ( - 7) * 3

= x2 - 4x - 21 

(ii) (ax + b)(cx + d) = acx? + (ad + bc)x+ bd e.g. (1) (2x + 3)(4x + 5) = (2 x 4 )x+ +(2 x 5+3 x 4)x+ 3 x 5

= 8x2 + 22x + 15 (2) (3x + 2)(5x – 7)

= (3 x 5 )x2 + [3 x ( - 7) + 2 x 5 x + 2 x ( - 7) = 15x2 + (-21 +10)x - 14 = 15x? - 11x - 14.