Factor completely. Hint: Factor out the GCF first.
$12x^2+48x+48$

• A. $12\(\left\)(x+2\(\right\))^2$
• B. $12\(\left\)(x+4\(\right\))^2$
• C. $12x\(\left\)(x+2\(\right\))^2$
• D. $12x\(\left\)(x+4\(\right\))^2$

Answer: (A)

Verified step by step guidance

1. Identify the general form of a perfect square trinomial, which is either \(a^{2} + 2ab + b^{2}\) or \(a^{2} - 2ab + b^{2}\).
2. Look at the given trinomial and check if the first and last terms are perfect squares. For example, check if the first term is a perfect square like \(a^{2}\) and the last term is a perfect square like \(b^{2}\).
3. Verify if the middle term matches \$2ab\( or \)-2ab$ by taking the square roots of the first and last terms and multiplying them by 2, considering the sign.
4. If the trinomial fits the pattern, rewrite it as the square of a binomial: \((a + b)^{2}\) if the middle term is positive, or \((a - b)^{2}\) if the middle term is negative.
5. Expand your binomial to check your work by using the formula \((a \\pm b)^{2} = a^{2} \\pm 2ab + b^{2}\) to ensure it matches the original trinomial.