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Question

# Factorise the given expression: xyâˆ’pq+qyâˆ’px

A

(py)(x+q)

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B

(yp)(x+q)

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C

(yp)(xq)

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D

(yx)(p+q)

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Solution

## 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) ⇒ xy−pq+qy−px=(y−p)(x+q) Therefore, the factors of xy−pq+qy−px are (y−p) and (x+q).

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