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Addition of Polynomials

a 2+4 ab +4 b...

Question

$a^{2} + 4 a b + 4 b^{2} - 9 m^{2} + 6 m n - n^{2}$

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Solution

$We have a^{2} + 4 a b + 4 b^{2} - 9 m^{2} + 6 m n - n^{2} = (a^{2} + 4 a b + 4 b^{2}) - (9 m^{2} - 6 m n + n^{2}) = [{(a)}^{2} + 2 \times a \times 2 b + {(2 b)}^{2}] - [{(3 m)}^{2} - 2 \times 3 m \times n + {(n)}^{2}] = {(a + 2 b)}^{2} - {(3 m - n)}^{2} = [(a + 2 b) + (3 m - n)] [(a + 2 b) - (3 m - n)] = (a + 2 b + 3 m - n) (a + 2 b - 3 m + n)$

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