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

$(x + y) (a x + b y)$

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$(x - y) (a x - b y)$

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$(x + y) (a x - b y)$

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$(a x + b y) (a x + b y)$

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Solution

The correct option is A
$(x + y) (a x + b y)$

The given expression
$a x^{2} + b y^{2} + b x y + a x y,$
can be rearranged as
$a x^{2} + a x y + b y^{2} + b x y$
Taking 'ax' common from the first two-terms and 'by' common from the last two-terms, we get
$= a x (x + y) + b y (y + x)$
$= (x + y) (a x + b y)$

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