Question

Factorise
(i) $x^2+xy+8x+8y$
(ii) $15xy-6x+5y-2$
(iii) $ax+by-ay-by$
(iv) $15pq+15+9q+25p$
(v) $z-7+7xy-xyz$

Answer 1

(i) $x^2+xy+8x+8y$
$=x(x+y)+8(x+y)$
$=(x+8)(x+y)$
(ii) $15xy-6x+5y-2$
$=3x(5y-2)+1(5y-2)$
$=(3x+1)(5y-2)$
(iii) $ax+by-ay-by$
$=x(a+b)-y(a+b)$
$=(x-y)(a+b)$
(iv) $15pq+15+9q+25p$
$=3q(5p+3)+5(5p+3)$
$=(3q+5)(5p+3)$
(v) $z-7+7xy-xyz$
$=z(1-xy)-7(1-xy)$
$=(z-7)(1-xy)$