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Question
Evaluate the following using identities:
`(a^2b - b^2a)^2`
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Solution
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`
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