Question

Factorise the expression
(i) $a{x}^2+bx$
(ii) $7p^2+21q^2$
(iii) $2x^3+2x{y}^2+2x{z}^2$
(iv) $a{m}^2+b{m}^2+b{n}^2+a{n}^2$
(v) $(lm+l)+m+1$
(vi) $y(y+z)+9(y+z)$
(vii) $5y^2-20y-8z+2yz$
(viii) $10ab+4a+5b+2$
(ix) $6xy-4y+6-9x$

Answer 1

(i) $a{x}^2+bx$

$=x(ax+b)$

(ii) $7p^2+21q^2$

$=7(p^2+3q^2)$

(iii) $2x^3+2x{y}^2+2x{z}^2$

$=2x(x^2+y^2+z^2)$

(iv) $a{m}^2+b{m}^2+b{n}^2+a{n}^2$

$=m^2(a+b)+n^2(a+b)$

$=(a+b)(m^2+n^2)$

(v) $(lm+l)+m+1$

$=(l+1)(m+1)$

(vi) $y(y+z)+9(y+z)$

$=(y+z)(y+9)$

(vii) $5y^2-20y-8z+2yz$

$=(y-4)(5y+2z)$

(viii) $10ab+4a+5b+2$

$=(2a+1)(5b+2)$

(ix) $6xy-4y+6-9x=3x(2y-3)-2(2y-3)$

$=(2y-3)(3x-2)$