Which of the following is equivalent to $(x + y + 3) (x + y + 3)$ ?

(x + y)^{2} + 9

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x^{2} + y^{2} + 9

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x^{2} + y^{2} + 6 x y + 9

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(x + y)^{2} + 6 (x + y) + 9

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(x + y)^{2} + 9 (x + y) + 9

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Solution

The correct option is E $(x + y)^{2} + 6 (x + y) + 9$
We need to simplify: $(x + y + 3) (x + y + 3)$
Put $x + y = t$
$∴ (t + 3) (t + 3) = t^{2} + 6 t + 9$
Again resubstitute $t = x + y$ , we get
${(x + y)}^{2} + 6 (x + y) + 9$

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