Question

Evaluate the following using suitable identities: (i) (99)^3 (ii) (102)^3

Answer 1

Answer:

1)970299

2)1061208

Explanation:

To solve this we must know:-

$\sf{}(a+b)^3=a^3+b^3+3ab(a+b)$

$\sf{}(a-b)^3=a^3-b^3-3ab(a-b)$

So,

(i) (99)³ = (100 - 1)³

= (100)³ - (1)³ - 3(100) (1) (100 - 1)

= 1000000 - 1 - 300(99)

= 1000000 - 1 - 29700

= 970299

(ii) (102)³ = (100 + 2)³

= (100)³ + (2)3 + 3(100) (2) (100 + 2)

= 1000000 + 8 + 600 (102)

= 1000000 + 8 + 61200

= 1061208

Answer 2

Step-by-step explanation:

99^3 = (100-1)^3

using identity (a-b)^3= a^3-b^3-3ab(a-b)

(100-1)^3= 100^3-1^3-3*100*1*(100-1)

=1000000-1-300*99

=1000000-1-29700

1000000-29701

=970299.

similarly, we can solve 100^3 by using the identity

(a+b)^3=a^3+b^3+3ab(a+b)