Question

Factorise
(i) $4p^2-9q^2$
(ii) $63a^2-112b^2$
(iii) $49x^2-36$
(iv) $16x^5-144x^3$
(v) $(l+m{)}^2-(l-m{)}^2$
(vi) $9x^2{y}^2-16$
(vii) $(x^2-2xy+y^2)-z^2$
(viii) $25a^2-4b^2+28bc-49c^2$

Answer 1

(i) $4p^2-9q^2$

$=(2p{)}^2-(3q{)}^2$
$=(2p+3q)(2p-3q)$
(ii) $63a^2-112b^2$

$=7\left[\right(3a{)}^2-\left(4b{)}^2\right]$
$=7(3a+4b)(3a-4b)$
(iii) $49x^2-36$

$=\left[\right(7x{)}^2-\left(6{)}^2\right]$
$=(7x-6)(7x+6)$
(iv) $16x^5-144x^3$

$=16x^3[x^2-3^2]$
$=16x^3(x-3)(x+3)$
(v) $(l+m{)}^2-(l-m{)}^2$

$=2m\times 2l=4lm$
(vi) $9x^2{y}^2-16$

$=\left[\right(3xy{)}^2-4^2]$
$=(3xy-4)(3xy+4)$
(vii) $(x^2-2xy+y^2)-z^2$

$=\left[\right(x-y{)}^2-z^2]$
$=(x-y+z)(x-y-z)$
(viii) $25a^2-4b^2+28bc-49c^2$

$=(5a{)}^2-[(2b-7c{)}^2]$
$=(5a+2b-7c)(5a-2b+7c)$