Factorise $a x^{2} y + b x y^{2} + c x y z$

x (a x + b y + c z)

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y (a x - b y - c z)

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x y (a x + b y + c z)

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x y (a + b y + c z)

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Solution

The correct option is D $x y (a x + b y + c z)$
We have, $a x^{2} y = a \times x \times x \times y$
$b x y^{2} = b \times x \times y \times y$
and, $c x y z = c \times x \times y \times z$
The three terms have x and y as common factors
$∴ a x^{2} y + b x y^{2} + c x y z = (a \times x \times x \times y) + (b \times x \times y \times y) + (c \times x \times y \times z)$
$= x \times y \times (a \times x + b \times y + c \times z)$
$= x y (a x + b y + c z)$

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