Asked by Sally
Write in factored form by factoring out the greatest common factor.
8 mn cubedplus152 m squared n cubed
8 mn cubedplus152 m squared n cubed
Answers
Answered by
GPT-4o mini
To factor the expression \( 8mn^3 + 152m^2n^3 \), we first need to identify the greatest common factor (GCF) of the two terms.
1. **Identify the coefficients**: The coefficients are 8 and 152. The GCF of 8 and 152 is 8.
2. **Identify the variable components**:
- The first term has \( mn^3 \) and the second term has \( m^2n^3 \).
- The common factors in terms of variables are \( m \) (since the first term has \( m^1 \) and the second term has \( m^2 \)) and \( n^3 \) (both terms have \( n^3 \)).
3. **Combine the GCF**: The GCF of the entire expression is \( 8mn^3 \).
Now we can factor this out:
\[
8mn^3 + 152m^2n^3 = 8mn^3(1 + 19m)
\]
Thus, the expression in factored form is:
\[
\boxed{8mn^3(1 + 19m)}
\]
1. **Identify the coefficients**: The coefficients are 8 and 152. The GCF of 8 and 152 is 8.
2. **Identify the variable components**:
- The first term has \( mn^3 \) and the second term has \( m^2n^3 \).
- The common factors in terms of variables are \( m \) (since the first term has \( m^1 \) and the second term has \( m^2 \)) and \( n^3 \) (both terms have \( n^3 \)).
3. **Combine the GCF**: The GCF of the entire expression is \( 8mn^3 \).
Now we can factor this out:
\[
8mn^3 + 152m^2n^3 = 8mn^3(1 + 19m)
\]
Thus, the expression in factored form is:
\[
\boxed{8mn^3(1 + 19m)}
\]