Prove that :
$(3 x - 2 y)^{2} + 24 x y = (3 x + 2 y)^{2}$

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Solution

To prove: $(3 x - 2 y)^{2} + 24 x y = (3 x + 2 y)^{2}$

On solving LHS we get
$(3 x - 2 y)^{2} + 24 x y$
$= (3 x)^{2} + (2 y)^{2} - 2 \times 3 x \times 2 y + 24 x y$
$= 9 x^{2} + 4 y^{2} - 12 x y + 24 x y$
$= 9 x^{2} + 4 y^{2} + 12 x y$
$= (3 x)^{2} + (2 y)^{2} + 2 \times 3 x \times 2 y$
$= (3 x + 2 y)^{2}$
$= R H S$
Hence, proved.

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