Question

4) Use formula to find the value of
i) (102)2 ii) 102 x 98​

Answer 1

Answer:

Using the identity (x+a)(x+b) = x

2

+(a+b)x+ab

Writing 102 as 100+2 and 98 as 100−2

Hence (100+2)(100−2) = 100

2

+[2+(−2)]100+(2)(−2)

= 10000+(0)100−4

= 9996

The answer is 9996

Answer 2

I) 10404

ii) 9996

Step-by-step explanation:

I) It is known that, ( a+b )² = a² + 2ab + b² and ( a - b )² =

a² - 2ab + b²

= (102)²

= ( 100 + 2 )²

= (100)² + 2 × 100 × 2 + (2)²

= 10000 + 400 + 4

= 10404

ii) Using the identity (x+a)(x+b) = x

2

+(a+b)x+ab

Writing 102 as 100+2 and 98 as 100−2

Hence (100+2)(100−2) = 100

2

+[2+(−2)]100+(2)(−2)

= 10000+(0)100−4

= 9996