Question

Evacuate each of the following using identities :
1. 105*95
2. 204*204
3. 96*96
4. 165*165-135*135​

Answer 1

1.) 105x95

= (100+5)X(100-5)

= using (a+b)(a-b)=a²-b²

= (100)²-(5)²

= 10000-25

= 9975.

2.) 204x204

= (200+4)x(200+4)

= using identity:- (a+b)²= a²+b²+2ab

= (200+4)²

= 40000+16+1600

= 41616

3.) 96x96

= (100-4)x(100-4)

= using identity:- (a-b)²= a²+b²-2ab

= (100-4)²

= 10000+16-800

= 9200+16

= 9216.

4.) 165x165-135x135

= (165)²-(135)²

= using identity:- a²-b²=(a+b)(a-b)

= (165+135)(165-135)

= 300x30

= 9000.

Hope it helps you.