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Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise a...

Question

Factorise $a^{2} + b^{2} + 2 (a b + b c + c a)$

A

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

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B

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

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C

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

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D

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

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Solution

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

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