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Question

Factorise: $$\displaystyle \left ( 2x-y \right )^{2}-14x+7y-18$$


A
(xy9)(2xy2)
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B
(2xy9)(2xy+7)
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C
(xy9)(2xy+7)
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D
(2xy9)(2xy+2)
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Solution

The correct option is D $$\displaystyle \left ( 2x-y-9 \right ) \left ( 2x-y+2 \right )$$
$$\left ( 2x-y \right )^{2}-14x+7y-18$$
$$=\left ( 2x-y \right )^{2}-7(2x-y)-18$$
Let $$2x-y=a$$
$$=a^2-7a-18$$
$$=a^2-9a+2a-18$$
$$=a(a-9)+2(a-9)$$
$$=(a-9)(a+2)$$
Putting the value of $$a$$,

$$(2x-y-9)(2x-y+2)$$

Mathematics

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