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 $8m{n}^3+152m^2{n}^3$, 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 $m{n}^3$ and the second term has $m^2{n}^3$.
   • 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 $8m{n}^3$.

Now we can factor this out:

$$8m{n}^3+152m^2{n}^3=8m{n}^3(1+19m)$$

Thus, the expression in factored form is:

$$\boxed{{\displaystyle 8m{n}^3(1+19m)}}$$