Match the following algebraic expressions with their factorised form.

x (3 x + 5)

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(2 x + 6)^{2}

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(x - 4) (x + 4)

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5 x (2 x^{3} + 6 x^{2} + 1)

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Solution

$3 x^{2} + 5 x = 3 \times x \times x + 5 \times x$
$= x (3 x + 5)$

In $10 x^{4} + 30 x^{3} + 5 x, 5 x$ is the common factor which can be taken as common. We get
$5 x (2 x^{3} + 6 x^{2} + 1)$ .

$x^{2} - 16$
= $x^{2} - 4^{2}$
= $(x - 4) (x + 4)$
Using identity $a^{2} - b^{2} = (a - b) (a + b)$

Using identity $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ,
$4 x^{2} + 24 x + 36$
= $(2 x)^{2} + 2 \times 2 x \times 6 + 6^{2}$
= $(2 x + 6)^{2}$

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