Find the combined product of (a^{4}+b^{4})(a^ | vedclass

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(D) Given expression: $(a^{4}+b^{4})(a^{2}+b^{2})(a+b)(a-b)$Step $1$: Use the identity $(a+b)(a-b) = a^{2}-b^{2}$.So,$(a+b)(a-b) = a^{2}-b^{2}$.Step $

Vedclass · Accepted Answer

$a^{8}-b^{8}$

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(D) Given expression: $(a^{4}+b^{4})(a^{2}+b^{2})(a+b)(a-b)$Step $1$: Use the identity $(a+b)(a-b) = a^{2}-b^{2}$.So,$(a+b)(a-b) = a^{2}-b^{2}$.Step $2$: Substitute this into the expression:$(a^{4}+b^{4})(a^{2}+b^{2})(a^{2}-b^{2})$Step $3$: Use the identity $(x+y)(x-y) = x^{2}-y^{2}$ where $x=a^{2}$ and $y=b^{2}$:$(a^{2}+b^{2})(a^{2}-b^{2}) = (a^{2})^{2}-(b^{2})^{2} = a^{4}-b^{4}$.Step $4$: Now multiply the remaining terms:$(a^{4}+b^{4})(a^{4}-b^{4})$Step $5$: Apply the identity $(x+y)(x-y) = x^{2}-y^{2}$ again where $x=a^{4}$ and $y=b^{4}$:$(a^{4})^{2}-(b^{4})^{2} = a^{8}-b^{8}$.

Find the combined product of $(a^{4}+b^{4})(a^{2}+b^{2})(a+b)(a-b)$.

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