Factor completely. Hint: Factor out the GCF first.
$-4y^3-24y^2-36y$

• A. $4y(y+6)(y+1)$
• B. $4y{(y+3)}^2$
• C. $36y{(y+1)}^2$
• D. $-4y{(y+3)}^2$

Answer: (D)

Verified step by step guidance

1. Identify the general form of a perfect square trinomial, which is either \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\). These can be factored as \((a + b)^2\) or \((a - b)^2\) respectively.
2. Look at the given trinomial and check if the first and last terms are perfect squares. For example, determine if the first term is a square of some expression \(a^2\) and the last term is a square of some expression \(b^2\).
3. Check the middle term to see if it matches \$2ab\( or \)-2ab\(, where \)a\( and \)b$ are the square roots of the first and last terms. This confirms whether the trinomial is a perfect square.
4. Once confirmed, write the factorization as \((a + b)^2\) if the middle term is positive, or \((a - b)^2\) if the middle term is negative.
5. If the trinomial is not a perfect square, explain that it cannot be factored as a perfect square trinomial and suggest other factoring methods if applicable.