Simplify : $(2 x + 5)^{2} - (2 x - 5)^{2}$

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Solution

$(2 x + 5)^{2} - (2 x - 5)^{2}$
$= (2 x)^{2} + 2 \times 2 x \times 5 + (5)^{2} - [(2 x)^{2} - 2 \times 2 x \times 5 + (5)^{2}]$
$[U s i n g i d e n t i t i e s (a + b)^{2} = a^{2} + 2 a b + b^{2} a n d (a - b)^{2} = a^{2} - 2 a b + b^{2}]$ $= 4 x^{2} + 20 x + 25 - [4 x^{2} - 20 x + 25]$
$= 40 x$

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