Question

Factorise the given expression:
$xy-pq+qy-px$

• A. $(p-y)(x+q)$
• B. $(y-p)(x+q)$
• C. $(y-p)(x-q)$
• D. $(y-x)(p+q)$

Answer 1

The correct option is B

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

Consider the given expression,

$xy-pq+qy-px$...(i)

By suitably rearranging the terms in (i), we get

$(xy-px)+(qy-pq)$...(ii)

Taking $x$ common from first two terms and $q$ common from last two terms, (ii) becomes

$=x(y-p)+q(y-p)$...(iii)

Taking $(y-p)$ common from (iii), we get

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

$\Rightarrow$ $xy-pq+qy-px$$=(y-p)(x+q)$

Therefore, the factors of $xy-pq+qy-px$ are $(y-p)$ and $(x+q)$.