Find the square of the following : $3 x + 4 y$

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Solution

Step 1 : First we need to identify the identity we can use, here we need to find the square, so we can use ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$
Step 2 : Now if we compare the question with the identity we get $a = 3 x, b = 4 y$
${(3 x + 4 y)}^{2} = {(3 x)}^{2} + 2 (3 x) (4 y) + {(4 y)}^{2} = 9 x^{2} + 24 x y + {16 y}^{2}$
Hence the square of $3 x + 4 y$ is $9 x^{2} + 24 x y + {16 y}^{2}$

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