Multiply using special products (7a - 8b)(2b + 7a)

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Solution

We can not apply any identity in this question. If it was (7a - 8b)(7a + 8b) then we can apply $(p + q) (p - q) = p^{2} - q^{2}$
i.e. $49 a^{2} - 64 b^{2}$
Else we can $(7 a - 8 b) (2 b + 7 a) = (7 a - 8 b) (7 a + 8 b - 6 b) = (7 a - 8 b) (7 a + 8 b) - (7 a - 8 b) (6 b) = 49 a^{2} - 64 b^{2} - 42 a b + 48 b^{2}$
$= 49 a^{2} - 16 b^{2} - 42 a b$

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