Question

$9(x + y) { }^{2} - x {}^{2}$
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Answer 1

Answer:

$9(x + y) {}^{2} - x {}^{2} \\ = (3(x + y)) {}^{2} - x {}^{2}$

We know

$a {}^{2} - b {}^{2} = (a + b)(a - b)$

Here

a= 3(x + y) and b = x

So

$9(x + y) {}^{2} - x {}^{2} \\ = (3(x + y)) {}^{2} - x {}^{2} \\ = (3(x + y) + x)(3(x + y) - x) \\ = (3x + 3y + x)(3x + 3y - x) \\ = (4x + 3y)(2x + 3y)$

Answer 2

Answer:

$9\left(x+y\right)^2-x^2\\= 9\left(x^2+2xy+y^2\right)-x^2\\= 9x^2+18xy+9y^2-x^2\\= 8x^2+18xy+9y^2$

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