Factorise the following by grouping the terms:
g) $4 a b x^{2} + 49 a b y^{2} + 14 x y (a^{2} + b^{2})$

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Solution

Given: $4 a b x^{2} + 49 a b y^{2} + 14 x y (a^{2} + b^{2})$

$= 4 a b x^{2} + 49 a b y^{2} + 14 a^{2} x y + 14 b^{2} x y$

On grouping the terms,

$= (4 a b x^{2} + 14 a^{2} x y) + (14 b^{2} x y + 49 a b y^{2})$

$= 2 a x (2 b x + 7 a y) + 7 b y (2 b x + 7 a y)$

$= (2 b x + 7 a y) (2 a x + 7 b y)$

Hence, the answer is $(2 b x + 7 a y) (2 a x + 7 b y)$ .

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