Evaluate $(2 x + 5)^{2} - (2 x - 5)^{2}$

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Solution

Given $(2 x + 5)^{2} - (2 x - 5)^{2}$
Since, we have $a^{2} - b^{2} = (a - b) (a + b)$
Substitute $a = 2 x + 5$ and $b = 2 x - 5$ , we get
$(2 x + 5)^{2} - (2 x - 5)^{2} = (2 x + 5 - (2 x - 5)) (2 x + 5 + 2 x - 5)$
$= (2 x + 5 - 2 x + 5) (2 x + 2 x)$
$= 10 (4 x)$
$= 40 x$
Therefore, the value of given expression is $40 x$ .

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