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Factorisation by Regrouping Terms

Factorise : 4...

Question

Factorise : $49 (x - y)^{2} - 9 (2 x + y)^{2}$

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Solution

$49 (x - y)^{2} - 9 (2 x + y)^{2} = [7 (x - y)]^{2} - [3 (2 x + y)]^{2} = (7 x - 7 y)^{2} - (6 x + 3 y)^{2} = (7 x - 7 y + 6 x + 3 y) (7 x - 7 y - 6 x - 3 y) = (13 x - 4 y) (x - 10 y)$

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Factorisation by Regrouping Terms

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