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Expansion of (a + b)^2

Simplify 4 ...

Question

Simplify $(4 x + 3) (4 x + 3) - (3 x + 6) (3 x - 6) - (2 x + 5) (2 x + 5)$

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Solution

Consider
$(4 x + 3)^{2} - (3 x + 6) (3 x - 6) - (2 x + 5) (2 x + 5)$
$\Rightarrow (4 x + 3)^{2} - (3 x + 6) (3 x - 6) - (2 x + 5)^{2}$
$\Rightarrow 16 x^{2} + 9 + 24 x - 9 x^{2} + 36 - 4 x^{2} - 25 - 20 x$
$\Rightarrow 3 x^{2} + 4 x + 20$

Identities used:
$1. (a + b)^{2} = a^{2} + 2 a b + b^{2}$
$2. a^{2} - b^{2} = (a - b) (a + b)$

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