Question

Factorise the following :
$\begin{array}{c}\left(i\right)6a+6b\\ \left(ii\right)ax+bx\\ \left(iii\right)3x^2-6a^6\end{array}$
$\begin{array}{c}\left(iv\right)9x^2+3x\\ \left(v\right)12x^{3}y-4x{y}^2\end{array}$
$\begin{array}{c}\left(vi\right)\frac{1}{2}x+\frac{1}{2}\\ \left(vii\right)cdm+cdt\\ \left(viii\right)36a^2{b}^3-18a^3{b}^2\\ \left(ix\right)25m^2{n}^3-5mn\\ \left(x\right)3ay+3az\end{array}$
$\begin{array}{c}\left(xi\right)185a+185b\\ \left(xii\right)28x-14y\\ \left(xiii\right)ax-ay\\ \left(xiv\right)12y^3+6a^3\\ \left(xv\right)3x+9y\end{array}$

Answer 1

(i) $6a+6b=6(a+b)$

(ii) $ax+bx=(a+b)x$

(iii) $3x^2-6a^6=3(x^2-2a^6)=3(x-\sqrt{2}{a}^3)(x+\sqrt{2}{a}^3)$

(iv) $9x^2+3x=3x(3x+1)$

(v) $12x^{3}y-4x{y}^2=4xy(3x^2-y)$

(vi) $\frac{1}{2}x+\frac{1}{2}=\frac{1}{2}(x+1)$

(vii) $cdm+cdt=cd(m+t)$

(viii) $36a^2{b}^3-18a^3{b}^2=18a^2{b}^2(2b-a)$

(ix) $25m^2{n}^3-5mn=5mn(5m{n}^2-1)$

(x) $3ay+3az=3a(y+z)$

(xi) $185a+185b=185(a+b)$

(xii) $28x-14y=14(2x-y)$

(xiii) $ax-ay=a(x-y)$

xiv) $12y^3+6a^3=6(2y^3+a^3)$

(xv) $3x+9y=3(x+3y)$