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Factorising a Binomial

Factorise:2 x...

Question

Factorise:
$2 x p + 4 x q - 3 y p - 6 y q$

A

$(p + 2 q) (2 x - 3 y)$

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B

$(p - 2 q) (2 x - 3 y)$

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C

$(p + 2 q) (2 x + 3 y)$

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D

$(p - 2 q) (2 x + 3 y)$

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Solution

The correct option is A
$(p + 2 q) (2 x - 3 y)$

The expression $2 x p + 4 x q - 3 y p - 6 y q$ can be regrouped as,

$(2 x p + 4 x q) + (- 3 y p - 6 y q)$

Taking $2 x$ and $- 3 y$ common, we get

$= 2 x (p + 2 q) - 3 y (p + 2 q)$

Taking $p + 2 q$ cmmon, we get
$= (p + 2 q) (2 x - 3 y)$

$\Rightarrow$ $2 x p + 4 x q - 3 y p - 6 y q$ $= (p + 2 q) (2 x - 3 y)$

Therefore, the factors of $2 x p + 4 x q - 3 y p - 6 y q$ are $(p + 2 q)$ and $(2 x - 3 y)$ .

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