Asked by fish
4.
Factor the expression.
4b2 + 28b + 49
(2b − 7)2
(−2b − 7)2
(2b + 7)2
(−2b + 7)2
Factor the expression.
4b2 + 28b + 49
(2b − 7)2
(−2b − 7)2
(2b + 7)2
(−2b + 7)2
Answers
Answered by
GPT-4o
To factor the expression \(4b^2 + 28b + 49\), we should look for a pattern or use factoring techniques. In this case, notice that the expression resembles a perfect square trinomial. A perfect square trinomial is of the form \((ax + b)^2\).
Let's consider:
\[ 4b^2 + 28b + 49 \]
We can rewrite the middle term (28b) as twice the product of the square root of the first term (\(4b^2\)) and the square root of the third term (\(49\)):
\[ 4b^2 + 28b + 49 = (2b)^2 + 2(2b)(7) + 7^2 \]
Recognizing that this matches the form \((a x + b)^2\), we can see that:
\[ 4b^2 + 28b + 49 = (2b + 7)^2 \]
Thus, the factorization of the expression is:
\[ (2b + 7)^2 \]
Therefore, the correct factorization from the given options is:
\[ \boxed{(2b + 7)^2} \]
Let's consider:
\[ 4b^2 + 28b + 49 \]
We can rewrite the middle term (28b) as twice the product of the square root of the first term (\(4b^2\)) and the square root of the third term (\(49\)):
\[ 4b^2 + 28b + 49 = (2b)^2 + 2(2b)(7) + 7^2 \]
Recognizing that this matches the form \((a x + b)^2\), we can see that:
\[ 4b^2 + 28b + 49 = (2b + 7)^2 \]
Thus, the factorization of the expression is:
\[ (2b + 7)^2 \]
Therefore, the correct factorization from the given options is:
\[ \boxed{(2b + 7)^2} \]