Factorise the following by taking out the common factors:
g) $2 a (p^{2} + q^{2}) + 4 b (p^{2} + q^{2})$

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Solution

Given: $2 a (p^{2} + q^{2}) + 4 b (p^{2} + q^{2})$

The commom factor is $2 (p^{2} + q^{2})$ .

Dividing the above expresion by $2 (p^{2} + q^{2})$ , we get ,

$\frac{2 a (p^{2} + q^{2})}{2 (p^{2} + q^{2})} + \frac{4 b (p^{2} + q^{2})}{2 (p^{2} + q^{2})}$

$= a + 2 b$

$∴ 2 a (p^{2} + q^{2}) + 4 b (p^{2} + q^{2}) = 2 (p^{2} + q^{2}) (a + 2 b)$

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