Question

Using suitable identity evaluate the following:
(i) 983
(ii) 188 × 212

Answer 1

Answer:

I) 983

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

ii) 188 × 212

=(200-12) (200+12)

=(200)^2-(12)^2

=40000-144

= 39856

Answer 2

Answer:

(i) (98)3

(98)3 = (100 - 2)3

(100 - 2)3 is of the form (a - b)3

(a - b)3 = a3 - 3a2b + 3ab2 - b3

So, (100 - 2)3 = 1003 - 3 × 1002 × 2 + 3 × 100 × 22 - 23

= 1,000,000 - 60,000 + 1200 - 8 = 9,41,192

(ii) 188 × 212

188 × 212 = (200 - 12)(200 + 12)

The expression is of the form (a - b)(a + b)

(a - b)(a + b) = a2 - b2

So, (200 - 12)(200 + 12) = 2002 - 122

= 40,000 - 144 = 39856