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 \(a^{2} - 2ab + b^{2}\), where the trinomial can be factored into \((a + b)^{2}\) or \((a - b)^{2}\) respectively.
2. Look at the given trinomial and check if the first and last terms are perfect squares. For example, verify if the first term is a perfect square like \(a^{2}\) and the last term is a perfect square like \(b^{2}\).
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 respectively. This confirms 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, using the values of \(a\) and \(b\) found from the square roots.
5. If the trinomial does not fit the perfect square pattern, consider other factoring methods or verify if it can be rewritten to match the perfect square form.