Question

Factorise the following expressions: (viii) ab(x^2+y^2)+xy(a^2+b^2).​

Answer 1

Answer:

The answer is $(bx+ay)(ax+by)$

Step-by-step explanation:

Given expression is

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

Open the bracket and regroup the terms

$=abx^2+aby^2+xya^2+xyb^2\\=(abx^2+xya^2)+(aby^2+xyb^2)$

Factor both terms

$=ax(bx+ay)+by(ay+xb)$

Factor out the common terms

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