Question

Factorise the following expressions:
(i) $p^2+6p+8$
(ii) $q^2-10q+21$
(iii) $p^2+6p-16$

Answer 1

(i) $p^2+6p+8$

$=p^2+2p+4p+8$
$=p(p+2)+4(p+2)$
$=(p+2)(p+4)$

(ii) $q^2-10q+21$

$=q^2-7q-3q+21$
$=q(q-7)-3(q-7)$
$=(q-3)(q-7)$

(iii) $p^2+6p-16$

$p^2+8p-2p-16$
$=p(p+8)-2(p+8)$
$=(p+8)(p-2)$