Question

Evaluate using suitable identity (99)²

Answer 1

Answer:

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:

1) 99²

= (100 -1)²

= 100²- 2×100×1 + 1²               [(a – b)² = a² – 2ab + b² ]

= 10000 - 200 + 1

= 9801

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Answer 2

(99)²=(100-1)²

=Applying (a-b)²

=(100)²+(1)²-2(100)(1)

=10000+1-200

=9801