Factorise:
$ab(x^2+y^2)-xy(a^2+b^2)$

Given:

The given expression is $ab(x^2+y^2)-xy(a^2+b^2)$.

To do:

We have to factorise the given expression.

Solution:

$ab(x^2+y^2)-xy(a^2+b^2)=abx^2+aby^2-a^2xy-b^2xy$
$=abx^2-b^2xy+aby^2-a^2xy$

$=bx(ax-by)-ay(ax-by)$

$=(ax-by)(bx-ay)$

Therefore,

Factors of $ab(x^2+y^2)-xy(a^2+b^2)$ are $(ax-by)$ and $(bx-ay)$.

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Updated on: 10-Oct-2022

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