Question
Which expression is equivalent to 16w ^ 2 + 24w + 9 ?
Q
H (8w + 3) ^ 2
J (8w - 3) ^ 2
G (4w - 3) ^ 2
F (4w + 3) ^ 2
Q
H (8w + 3) ^ 2
J (8w - 3) ^ 2
G (4w - 3) ^ 2
F (4w + 3) ^ 2
Answers
GPT-4o mini
To determine which expression is equivalent to \( 16w^2 + 24w + 9 \), we can try to factor or rewrite it, possibly looking for it in the form of a perfect square trinomial.
We notice that the coefficients suggest a perfect square, specifically of the form \((aw + b)^2\).
Let's see if we can express \( 16w^2 + 24w + 9 \) in the form \((4w + 3)^2\):
1. The first term is \( (4w)^2 = 16w^2 \).
2. The last term is \( 3^2 = 9 \).
3. The middle term can be checked using the formula for the expansion of a square:
\[
(4w + 3)^2 = (4w)^2 + 2 \cdot (4w) \cdot 3 + 3^2 = 16w^2 + 24w + 9
\]
Since \( 16w^2 + 24w + 9 \) can be factored as \( (4w + 3)^2 \), this means that the equivalent expression is:
**F** \( (4w + 3)^2 \)
We notice that the coefficients suggest a perfect square, specifically of the form \((aw + b)^2\).
Let's see if we can express \( 16w^2 + 24w + 9 \) in the form \((4w + 3)^2\):
1. The first term is \( (4w)^2 = 16w^2 \).
2. The last term is \( 3^2 = 9 \).
3. The middle term can be checked using the formula for the expansion of a square:
\[
(4w + 3)^2 = (4w)^2 + 2 \cdot (4w) \cdot 3 + 3^2 = 16w^2 + 24w + 9
\]
Since \( 16w^2 + 24w + 9 \) can be factored as \( (4w + 3)^2 \), this means that the equivalent expression is:
**F** \( (4w + 3)^2 \)