I Have tried multiple sites such as Symbolab, Math Papa, and Mathway. But none of them can explain the relationship between

$$frac{a^8+8a^6b^2+14a^4b^4+8a^2b^6+b^8}{a^6+7a^4b^2+7a^2b^4+b^6} = a^2 + b^2$$

Yet when I plug in values for $a$ and $b$ it shows that the expressions are equivalent. I have even

tried using sites which are designed for proofing but none of them actually explain why the relationship is true.

Can someone please explain how this can be shown true? Any help would be much appreciated