Write in factored form by factoring out the greatest common factor.

Question

8 mn cubedplus152 m squared n cubed

Answer 1

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:

\[ \boxed{8mn^3(1 + 19m)} \]