Question

Evaluate using identity
a) (102)²
b) 95 × 105
c) 55² - 48²

Answer 1

• (102)²

= (100+2)²

= 100²+2×100×2+2²

= 10000+200+4

= 10204

• 95×105

= (100-5)(100+5)

= 100²-5²

= 10000-25

= 9975

Hope this helps you

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Answer 2

100 +2 )²

a) By using identity,

➡️( a + b ) ² = a ² + b ² + 2ab

Here, a = 100, b = 2.

( 100 +2 )² = 100² + 2² +2 *100 *2

= 10000 + 4 + 400

= 10404.

b) We can write 105 = 100 + 5 and 95 = 100 - 5 .

=  105 * 95

= ( 100 + 5 ) ( 100 - 5 )

( A + B ) ( A- B ) = A ^ 2 - B ^ 2.

By using this formula,

= 100 ^ 2 - 5 ^ 2

= 10,000 - 25

= 9,975

c) 721