Question

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

Answer 1

$i)p^2+6p+8=p^2+3\times 2p+9-9+8={(p+3)}^2-1=(p+3-1\left)\right(p+3+1)=(p+2\left)\right(p+4\left)ii\right)q^2-10q+21=q^2-5\times 2q+25-25+21={(q-5)}^2-2^2=(q-5-2)(q-5+2)=(q-7)(q-3)$