Question

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

• A. $(x-y-9)(2x-y-2)$
• B. $(2x-y-9)(2x-y+7)$
• C. $(x-y-9)(2x-y+7)$
• D. $(2x-y-9)(2x-y+2)$

Answer 1

The correct option is D $(2x-y-9)(2x-y+2)$

${(2x-y)}^2-14x+7y-18$

$={(2x-y)}^2-7(2x-y)-18$

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 $a$,

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