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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