Question

How do you factor completely `a^4-b^4`?

Answer 1

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

Explanation:

In algebra, there is a formula known as the Difference of two squares: `(a^2-b^2)=(a+b)(a-b)`

In the case of `a^4-b^4`, you'll see that `a^4` is just `(a^2)^2` and `b^4` is just `(b^2)^2`:
`a^4-b^4=(a^2)^2-(b^2)^2`
`=(a^2+b^2)(a^2-b^2)`
But as you can see, we can use the formula again:
`=(a^2+b^2)(a+b)(a-b)`
And this is the final answer