Evaluate the following algebraic identify:$(a+b)(a-b)(a^2-b^2)(a^2+b^2)$.

Given :

The given algebraic expression is $(a+b)(a-b)(a^2-b^2)(a^2+b^2)$.

To do :

We have to evaluate the given algebraic expression.

Solution :

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

Therefore, 

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

                                                     $= a^2(a^4-b^4) - b^2(a^4-b^4)$

                                                    $= a^6-a^2b^4-b^2a^4+b^6$

Therefore, $(a+b)(a-b)(a^2-b^2)(a^2+b^2)=a^6-a^2b^4-b^2a^4+b^6$.

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Updated on: 10-Oct-2022

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