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Algebraic Identities

Factorise the...

Question

Factorise the following by taking out the common factors:
b) $5 a (x^{2} - y^{2}) + 35 b (x^{2} - y^{2})$

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Solution

Given: $5 a (x^{2} - y^{2}) + 35 b (x^{2} - y^{2})$

The common factor is $5 (x^{2} - y^{2})$

Dividing by $5 (x^{2} - y^{2})$ in the above expression :

We get,

${\frac{5 a (x^{2} - y^{2})}{5 (x^{2} - y^{2})}}$ + ${\frac{35 b (x^{2} - y^{2})}{5 (x^{2} - y^{2})}}$

$= a + 7 b$

$∴ 5 a (x^{2} - y^{2}) + 35 b (x^{2} - y^{2})$
$= 5 (x^{2} - y^{2}) (a + 7 b)$ .

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