Question

"Question 7 Using a^2 − b^2 = (a + b) (a − b), find (i) 51^2 − 49^2 (ii) (1.02)^2 − (0.98)^2 (iii) 153^2 − 147^2 (iv) 12.1^2 − 7.9^2

Class 8 Algebraic Expressions and Identities Page 152"

Answer 1

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Answer 2

An identity is true only for certain values of its variables. An equation is not an identity.

The following are the identities

(a + b)² = a² + 2ab + b² 
(a – b)² = a² – 2ab + b² 
(a – b)(a + b) = a² – b²

 Another useful identity is

 (x + a) (x + b) = x² + (a + b) x + ab

If the given expression is the difference of two squares we use the formula

a² –b² = (a+b)(a-b)

 

• The above four identities are useful in carrying out squares and products of algebraic expressions. They also allow easy alternative methods to calculate products of numbers and so on.

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Solution:

Using a²– b²= (a + b) (a – b)

1) 51²– 49² 

= (51 + 49)(51 - 49)
= 100 x 2

= 200

2) (1.02)²– (0.98)²
= (1.02 + 0.98)(1.02 - 0.98)
= 2 x 0.04

= 0.08

3) 153²– 147²

= (153 + 147)(153 - 147)
= 300 x 6

= 1800

4) 12.1²– 7.9²

= (12.1 + 7.9)(12.1 - 7.9)
= 20 x 4.2

= 84

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