Factor the polynomial $y^4 - y^2 - 20$ using the substitution method.

Step 1: Identify that $(y^2)^2 = y^4$. Let $u = y^2$. Step 2: Substitute $u$ into the expression to create a standard quadratic trinomial: $u^2 - u - 20$ Step 3: Factor the quadratic trinomial. Find two numbers that multiply to $-20$ and add to $-1$. The numbers are $-5$ and $4$: $(u - 5)(u + 4)$ Step 4: Substitute $y^2$ back in place of $u$: $(y^2 - 5)(y^2 + 4)$ Step 5: Check the factorization by multiplying: $(y^2 - 5)(y^2 + 4) = y^4 + 4y^2 - 5y^2 - 20 = y^4 - y^2 - 20$ ✓

The factored form is $(y^2 - 5)(y^2 + 4)$.