Find the greatest common factor of the terms of the $$ 4 n^{3}+8 n^{2} $$

Question

UpStudy AI · Accepted Answer

We start with the expression:
$$
4n^3 + 8n^2
$$

**Step 1: Factor the Numerical Coefficients**

The numerical coefficients are 4 and 8. The greatest common factor (GCF) of 4 and 8 is:
$$
4
$$

**Step 2: Factor the Variable Part**

The variable factors are $$ n^3 $$ and $$ n^2 $$. The highest power common to both is:
$$
n^2
$$

**Step 3: Combine the Factors**

Thus, the overall GCF is:
$$
4n^2
$$

The expression can be factored as:
$$
4n^3 + 8n^2 = 4n^2(n + 2)
$$

Hence, the greatest common factor of the terms is:
$$
4n^2
$$
The greatest common factor of the terms $$4n^{3} + 8n^{2}$$ is $$4n^{2}$$.

Find the greatest common factor of the terms of the \[ 4 n^{3}+8 n^{2} \]