Which of the following is not a factor of $a x^{2} + b y^{2} + b x y + a x y ?$

a + b

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x + y

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ax + by

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Solution

The correct option is A
a + b

The expression is: $a x^{2} + b y^{2} + b x y + a x y$
There are no common factors in the first and the second term. So, we have to re-arrange the terms in order to find the common factors.
$a x^{2} + a x y + b y^{2} + b x y = a x (x + y) + b y (y + x)$
$= (x + y) (a x + b y)$

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

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a^{2} x^{2} + 2 h (a + b) x y + b^{2} y^{2} = 0

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