### Instruction: Factor $w^4-16$ as far as possible, where the factors are monic polynomials with real coefficients.### Response: Ok, so we want to factor $w^4-16$.
Right. Let's first rewrite it as $(w^2)^2-4^2$.
Now it looks like a difference of squares.
Exactly. So, we can rewrite it as $(w^2+4)(w^2-4)$.
But we're not done yet. We can still factor $w^2-4$.
Right. That's equal to $(w+2)(w-2)$.