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

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Solution

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

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