4.

Question

Factor the expression.

4b2 + 28b + 49

(2b − 7)2

(−2b − 7)2

(2b + 7)2

(−2b + 7)2

Answer 1

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 $(ax+b{)}^2$, 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:
$$\boxed{{\displaystyle (2b+7{)}^2}}$$