Evaluate each of the following using identities:$(a^2b - b^2a)^2$

Given:

$(a^2b - b^2a)^2$

To do:

We have to evaluate the given expression using a suitable identity.

Solution:

We know that,

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

$(a+b)(a-b)=a^2-b^2$
Therefore,

$(a^{2} b-b^{2} a)^{2}=(a^{2} b)^{2}+(b^{2} a)^{2}-2 \times a^{2} b \times  b^{2} a$

$=a^{4} b^{2}-2 a^{3} b^{3}+b^{4} a^{2}$

Hence, $(a^{2} b-b^{2} a)^{2}=a^{4} b^{2}-2 a^{3} b^{3}+b^{4} a^{2}$.

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Updated on: 10-Oct-2022

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