Factorise the following by grouping the terms:xy(a^2 + 1) + a(x^2… - Vidyadip

Question

Factorise the following by grouping the terms:$xy(a^2 + 1) + a(x^2 + y^2)$

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Answer

$xy(a^2 + 1) + a(x^2 + y^2)$
$= a^2xy + xy + ax^2 + ay^2$
$= (a^2xy + ax^2) + (ay^2 + xy)$
$= ax(ay + x) + y(ay + x)$
$= (ay + x)(ax + y).$

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