Question

Evaluate the following using identities:

`(a^2b - b^2a)^2`

Answer 1

In the given problem, we have to evaluate expressions by using identities.

The given expression is `(a^2b - b^2a)^2`

We shall use the identity `(x - y)^2 = x^2- 2xy + y^2`

Here `x = a^2b`

`y = b^2a`

By applying identity we get

`(a^2b - b^2a)^2 = (a^2b)^2 + (b^2a)^2 - 2 xx a^2b xx b^2a`

`= (a^2b xx a^2b) + (b^2a xx b^2a) - 2 xx a^2b xx b^2a`

`= a^4b^2 - 2a^3b^3 + b^4a^2`

Hence the value of `(a^2b - b^2a)^2  "is"  a^4b^2 - 2a^3b^3 + b^4a^2`