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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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