Question

Factorise each of the following algebraic expressions:
$i)3x+15$ $ii)2x^2+5x$ $iii)3x^{2}y-6x{y}^2$

Answer 1

(i) The greatest common factor of the terms namely, 3x and 15 of the expression 3x + 15 is 3. Also, 3x = 3 $\times$ x and 15 = $3\times 5$.
$\therefore 3x+15=3(x+5)$
(ii) $2x^2=2x\times xand5x=5\times x.$
$\therefore 2x^2+5x=2x\times x+5\times x=(2x+5)x$
(iii) Clearly, 3xy is the greatest common factor of the terms $3x^{2}yand6x{y}^2$ of the binomial
$3x^{2}y-6x{y}^2$.
Also,$3x^{2}y=3xy\times xand6x{y}^2=3xy\times 2y$
$\therefore 3x^{2}y-6x{y}^2=3xy\times x-3xy\times 2y=3xy(x-2y)$