Question

Use a special-product rule to factor the perfect-square trinomial.
y^4 - 6y^2 + 9

Answer 1

The factorization of the perfect-square trinomial is:
`(y^2 - 3)^2`

Explanation:

These two factorizations involve perfect-square trinomials.

`(x + y)^2 = x^2 + 2xy + y^2`

`(x - y)^2 = x^2 - 2xy + y^2`

In this question, we use the second. So

`y^4 - 6y^2 + 9 = (y^2 - 3)^2`

The factorization of the perfect-square trinomial is:
`(y^2 - 3)^2`