Questions: Completely factor the expression by grouping, if possible. 9ba - 5 - 4b^2 - 5b

Completely factor the expression by grouping, if possible. 9ba - 5 - 4b^2 - 5b
Transcript text: Completely factor the expression by grouping, if possible. \[ 9 b a-5-4 b^{2}-5 b \]
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Solution

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Solution Steps

Step 1: Rewrite the Expression

We start with the expression: \[ 9ab - 5 - 4b^2 - 5b \] Rearranging the terms gives us: \[ 9ab - 4b^2 - 5b - 5 \]

Step 2: Group the Terms

Next, we can group the terms in pairs: \[ (9ab - 4b^2) + (-5b - 5) \]

Step 3: Factor Out the Greatest Common Factor

Now, we factor out the greatest common factor from each group:

  1. From the first group \(9ab - 4b^2\), we can factor out \(b\): \[ b(9a - 4b) \]
  2. From the second group \(-5b - 5\), we can factor out \(-5\): \[ -5(b + 1) \]
Step 4: Combine the Factored Groups

After factoring, we have: \[ b(9a - 4b) - 5(b + 1) \] However, the resulting binomials do not match, indicating that the expression cannot be factored by grouping.

Final Answer

The expression \(9ab - 4b^2 - 5b - 5\) is not factorable by grouping. Thus, the final answer is: \[ \boxed{\text{Not Factorable By Grouping}} \]

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