Factorize:
$4 a^{2} - (4 b^{2} + 4 b c + c^{2})$ .

(a + b + c) (2 a - 2 b + c)

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(a + 2 b + c) (2 a - b - c)

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(a + b + c) (a - 3 b - c)

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(2 a + 2 b + c) (2 a - 2 b - c)

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Solution

The correct option is D $(2 a + 2 b + c) (2 a - 2 b - c)$
$4 a^{2} - (4 b^{2} + 4 b c + c^{2})$
$= (2 a)^{2} - ((2 b)^{2} + 2 (2 b) (c) + c^{2})$
$= (2 a)^{2} - (2 b + c)^{2}$
$= (2 a + 2 b + c) (2 a - 2 b - c)$

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Simplify:
$(a - 2 b + 5 c) (a - b) - (a - b - c) (2 a + 3 c) + (6 a + b) (2 c - 3 a - 5 b)$

(a - 2 b + 5 c) (a - b) - (a - b - c) (2 a + 3 c) + (6 a + b) (2 c - 3 a - 5 b)

19 c a - 37 a b - 19 a^{2}

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