Question

SOLVE USING IDENTITY :— (a) 99 x 101
(b) 98²

Answer 1

(a). 99 x 101 can be written as

(100-1)(100+1)

Using identity (a+b)(a-b)= a^2-b^2

100^2 - 1^2

10000-1

=9999

b.

${98}^{2}$

can be written as

${(100 - 2)}^{2}$

using identity

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

$10000 + 4 - 2 \times 100 \times 2$

$10004 - 400$

Answer will be 9604

Answer 2

a (100-1)(100+1)

using identity (a²-b²)=(a+b)(a-b)

∴(100-1)(100+1)=100²-1²

10000-1

9999

b (100-2)²

using identity (a-b)²=(a²+b²-2ab)

(100-2)²=(100²+2²-2*100*2)

10000+4-400

9604

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