Question

b^2 + 8b + 7
a. (b + 7) (b + 1)
b. (b + 1)(b - 7)
c. (b -1)(b + 7)
d. (b - 1)(b - 7)

Explanation:

Step1: Expand Option A

To check if \((b + 7)(b + 1)\) equals \(b^2 + 8b + 7\), we use the distributive property (FOIL method).
First, multiply the First terms: \(b\times b = b^2\).
Then, the Outer terms: \(b\times1 = b\).
Next, the Inner terms: \(7\times b = 7b\).
Finally, the Last terms: \(7\times1 = 7\).
Now, combine like terms: \(b^2 + b + 7b + 7 = b^2 + 8b + 7\), which matches the given quadratic expression.

Step2: Verify Other Options (Optional)

For Option B: \((b + 1)(b - 7)=b^2 - 7b + b - 7 = b^2 - 6b - 7
eq b^2 + 8b + 7\).
For Option C: \((b - 1)(b + 7)=b^2 + 7b - b - 7 = b^2 + 6b - 7
eq b^2 + 8b + 7\).
For Option D: \((b - 1)(b - 7)=b^2 - 7b - b + 7 = b^2 - 8b + 7
eq b^2 + 8b + 7\).

Answer:

A. \((b + 7)(b + 1)\)