Questions: Completely factor the expression by grouping, if possible. 8ba-7+2b^2-7b

Completely factor the expression by grouping, if possible. 8ba-7+2b^2-7b
Transcript text: Completely factor the expression by grouping, if possible. \[ 8 b a-7+2 b^{2}-7 b \]
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Solution

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Solution Steps

Step 1: Rearrange the terms

Rearrange the expression to group like terms together: \[ 8ba - 7 + 2b^2 - 7b = 2b^2 + 8ba - 7b - 7 \]

Step 2: Group the terms

Group the terms into two pairs: \[ (2b^2 + 8ba) + (-7b - 7) \]

Step 3: Factor out the greatest common factor (GCF) from each group

Factor out the GCF from each group: \[ 2b(b + 4a) - 7(b + 1) \]

Final Answer

\(\boxed{(2b - 7)(b + 4a + 1)}\)

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