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Solve the expression using identities $178 × 178 − 22 × 22$ .

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31200

32000

20000

12000

answer is A.

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Detailed Solution

Given expression is

178 × 178 − 22 × 22

.
Using the identity,

a + b a − b = a 2 − b 2

Consider, a=178 and b=22.

178 × 178 − 22 × 22 = 1782 − 222 ⇒ 178 × 178 − 22 × 22 = 178 + 22 178 − 22 ⇒ 178 × 178 − 22 × 22 = 200 × 156 ⇒ 178 × 178 − 22 × 22 = 31200

So, the value of

178 × 178 − 22 × 22

is 31200.
Hence, option 1 is correct.

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