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Answer
The factored form of \( ab + 6a - 3b - 18 \) is \( (a - 3)(b + 6) \).
Solution
To factor the expression \( ab + 6a - 3b - 18 \) by grouping, follow these steps:
1. **Group the terms:**
\[
ab + 6a - 3b - 18 = (ab + 6a) + (-3b - 18)
\]
2. **Factor out the common factors from each group:**
- From the first group \( (ab + 6a) \), factor out \( a \):
\[
a(b + 6)
\]
- From the second group \( (-3b - 18) \), factor out \( -3 \):
\[
-3(b + 6)
\]
3. **Factor out the common binomial factor \( (b + 6) \):**
\[
a(b + 6) - 3(b + 6) = (a - 3)(b + 6)
\]
So, the factored form of the expression is:
\[
(a - 3)(b + 6)
\]
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Simplify this solution Bonus Knowledge
To factor the expression \( ab + 6a - 3b - 18 \) by grouping, we can start by rearranging it as follows: 1. Group the terms: \( (ab - 3b) + (6a - 18) \). 2. Factor out the common factors within each group: - From the first group \( ab - 3b \), we can factor out \( b \): \( b(a - 3) \). - From the second group \( 6a - 18 \), we can factor out \( 6 \): \( 6(a - 3) \). Now we have: \[ b(a - 3) + 6(a - 3) \] 3. Notice that \( (a - 3) \) is a common factor: \[ (a - 3)(b + 6) \] So the expression factors to: \[ (a - 3)(b + 6) \] This is the factored form of the original expression!
