Question

find the products: (a²+b²)(a⁴+b⁴)(a+b)(a-b)​

Answer 1

Answer:

$\mathrm{Expand\:}\left(a^2+b^2\right)\left(a^4+b^4\right)\left(a+b\right)\left(a-b\right):\quad a^8-b^8$

Step-by-step explanation:

$\left(a^2+b^2\right)\left(a^4+b^4\right)\left(a+b\right)\left(a-b\right)$

$=\left(a^2+b^2\right)\left(a^4+b^4\right)\left(a^2-b^2\right)$

$=\left(a^4-b^4\right)\left(a^4+b^4\right)$

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}\left(a-b\right)\left(a+b\right)=a^2-b^2$

$\left(a^4-b^4\right)\left(a^4+b^4\right)=\left(a^4\right)^2-\left(b^4\right)^2$

$=\left(a^4\right)^2-\left(b^4\right)^2$

$=a^8-b^8$

Answer 2

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