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$5 {(x + y)}^{2} - 6 x - 6 y - 8$

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Solution

Let us solve the given expression $5 (x + y)^{2} - 6 x - 6 y - 8$ as shown below:

$5 (x + y)^{2} - 6 x - 6 y - 8 = 5 (x^{2} + y^{2} + 2 x y) - 6 x - 6 y - 8 (∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b) = 5 x^{2} + 5 y^{2} + 10 x y - 6 x - 6 y - 8$

Hence, $5 (x + y)^{2} - 6 x - 6 y - 8 = 5 x^{2} + 5 y^{2} + 10 x y - 6 x - 6 y - 8$ .

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