Question

$ab(x {}^{2} + y {}^{2} ) - xy(a { }^{2 } + b {}^{2} )$
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Answer 1

ANSWER:

To Simplify:

• ab(x² + y²) - xy(a² + b²)

Solution:

We are given that,

⇒ab(x² + y²) - xy(a² + b²)

Opening the brackets,

⇒abx² + aby² - a²xy - b²xy

Now, we will rearrange the terms, so that, we get something common to simplify the expression.

⇒(abx² - b²xy) + (aby² - a²xy)

Taking bx common in the first pair and ay in the second pair.

⇒bx(ax - by) + ay(by - ax)

Taking (-) common in the second pair,

⇒bx(ax - by) - ay(ax - by)

Now,

We will take (ax - by) common.

So,

⇒(ax - by)(bx - ay)

Hence, the simplified value of ab(x² + y²) - xy(a² + b²) is (ax - by)(bx - ay).