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+2b2−7b=2b2+8ba−7b−7 8ba - 7 + 2b^2 - 7b = 2b^2 + 8ba - 7b - 7

Step 2: Group the terms

Group the terms into two pairs: (2b2+8ba)+(−7b−7) (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) 2b(b + 4a) - 7(b + 1)

Final Answer

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

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