Expand (2x+3)(2x+5) using appropriate identity.

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Solution

Using the identity $(m + a) (m + b) = m^{2} + m (a + b) + a b$ .
Given, $(2 x + 3) (2 x + 5)$
We can apply the above identity by taking
$m = 2 x$ , $a = 3$ , $b = 5$ .
Hence, we get,
$(2 x + 3) (2 x + 5) = {(2 x)}^{2} + (2 x) (3 + 5) + (3 \times 5)$
$\Rightarrow 4 x^{2} + (2 x) (8) + 15$
$\Rightarrow 4 x^{2} + 16 x + 15$

Hence, $(2 x + 3) (2 x + 5) = 4 x^{2} + 16 x + 15$ .

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