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Factorisation

Factorise ...

Question

Factorise $4 a^{2} b - 12 a^{2} - 16 b + 48$

A

4xz

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B

4xy

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C

4xz

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D

4xyz

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Solution

The correct option is B
4xy

Given $4 a^{2} b - 12 a^{2} - 16 b + 48$

Taking common factor as $4 a^{2}$ from the first two terms and $16 b$ as from the last two terms we get

$4 a^{2} b - 12 a^{2} - 16 b + 48$ = $4 a^{2} (b - 3) - 16 (b - 3)$

= $(4 a^{2} - 16) (b - 3)$

= $(2 a)^{2} - (4)^{2}) (b - 3)$ ( converting in the form $a^{2} - b^{2})$

= $(2 a - 4) (2 a + 4) (b - 3))$

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