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$a m 2 − n 2 × a n 2 − m 2 =$

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$a m 2 + n 2$

$a 2 m 2 + 2 n 2$

answer is B.

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Detailed Solution

$a m 2 − n 2 × a n 2 − m 2$

$= a m 2 − n 2 + n 2 − m 2$

$= a 0$

$= 1$

$a m × a n = a m + n$

(or)

$a m 2 − n 2 × a n 2 − m 2$

$= a m + n m − n × a n + m n − m ∵ a 2 − b 2 = a + b a − b$

$= a m + n m − n × a m + n n − m ∵ a + b = b + a$

$= a m + n m − n + m + n n − m$

Here

$m + n$

is common

$m + n m − n + n − m$

$= a m + n 0$

$= a 0$

$= 1$

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