Question
Factor the expression completely 36ab^2 - 48a^2b
Answers
Answered by
GPT-4o mini
To factor the expression \( 36ab^2 - 48a^2b \), we first look for the greatest common factor (GCF) of the two terms.
1. **Identify the GCF**:
- The coefficients 36 and 48 have a GCF of 12.
- The variables have \( a \) and \( b \). The GCF considering the variables is \( ab \) (the lowest power of each variable in the expression).
Thus, the GCF of the expression is \( 12ab \).
2. **Factor out the GCF**:
We can factor \( 12ab \) out of each term in the expression:
\[
36ab^2 - 48a^2b = 12ab(3b) - 12ab(4a)
\]
This simplifies to:
\[
12ab(3b - 4a)
\]
3. **Final Factored Form**:
The expression \( 36ab^2 - 48a^2b \) factored completely is:
\[
\boxed{12ab(3b - 4a)}
\]
1. **Identify the GCF**:
- The coefficients 36 and 48 have a GCF of 12.
- The variables have \( a \) and \( b \). The GCF considering the variables is \( ab \) (the lowest power of each variable in the expression).
Thus, the GCF of the expression is \( 12ab \).
2. **Factor out the GCF**:
We can factor \( 12ab \) out of each term in the expression:
\[
36ab^2 - 48a^2b = 12ab(3b) - 12ab(4a)
\]
This simplifies to:
\[
12ab(3b - 4a)
\]
3. **Final Factored Form**:
The expression \( 36ab^2 - 48a^2b \) factored completely is:
\[
\boxed{12ab(3b - 4a)}
\]
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