Factorise: $x a^{2} + y b^{2} + y a^{2} + x b^{2}$

(x + y) (a^{2} + b^{2})

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(x^{2} + y^{2}) (a + b)

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(x^{2} + a^{2}) (y^{2} + b^{2})

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(x + a^{2}) (y + b^{2})

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Solution

The correct option is B $(x + y) (a^{2} + b^{2})$
$x a^{2} + y b^{2} + y a^{2} + x b^{2}$
$= x a^{2} + x b^{2} + y a^{2} + y b^{2}$ ...(Regrouping terms)
$= x (a^{2} + b^{2}) + y (a^{2} + b^{2})$
$= (a^{2} + b^{2}) (x + y)$
$= (x + y) (a^{2} + b^{2})$

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