Factorise the following:
9(x + y)2 - x2
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9(x + y)2 - x2 = [3(x + y)]2 - x2.
Using identity,
a2 - b2 = (a + b)(a - b).
[3(x + y)]2 - x2 = [3(x + y) - x][3(x + y) + x] = (3x + 3y + x)(3x + 3y - x) = (4x + 3y)(2x + 3y).
Hence, 9(x + y)2 - x2 = (4x + 3y)(2x + 3y).
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