Using special products, simplify :
${(x + 0.4 y)}^{2}$

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Solution

Step 1: Identification of identity
First we need to identify the identity we can use,
Here we need to find the square, so we can use ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$
Now if we compare the question with the identity we get $a = x, b = 0.4 y$
Step 2: Applying the formula
${(x + 0.4 y)}^{2} = x^{2} + 2 (x) (0.4 y) + {(0.4 y)}^{2} = x^{2} + 0.8 x y + {0.16 y}^{2}$
Hence, the square of ${(x + 0.4 y)}^{2}$ is $x^{2} + 0.8 x y + {0.16 y}^{2}$ .

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