Pre-Algebra Examples

$6 m^{3} n$ , $2 m^{5} n^{5} \cdot (2 m n^{3})$

Step 1

Factor $2 m^{3} n$ out of $6 m^{3} n + 2 m^{5} n^{5} \cdot (2 m n^{3})$ .

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Step 1.1

Factor $2 m^{3} n$ out of $6 m^{3} n$ .

$2 m^{3} n (3) + 2 m^{5} n^{5} \cdot (2 m n^{3})$

Step 1.2

Factor $2 m^{3} n$ out of $2 m^{5} n^{5} \cdot (2 m n^{3})$ .

$2 m^{3} n (3) + 2 m^{3} n (m^{2} n^{4} \cdot (2 m n^{3}))$

Step 1.3

Factor $2 m^{3} n$ out of $2 m^{3} n (3) + 2 m^{3} n (m^{2} n^{4} \cdot (2 m n^{3}))$ .

$2 m^{3} n (3 + m^{2} n^{4} \cdot (2 m n^{3}))$

Step 2

Combine exponents.

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Step 2.1

Raise $m$ to the power of $1$ .

$2 m^{3} n (3 + m^{1} m^{2} n^{4} \cdot (2 n^{3}))$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 m^{3} n (3 + m^{1 + 2} n^{4} \cdot (2 n^{3}))$

Step 2.3

Add $1$ and $2$ .

$2 m^{3} n (3 + m^{3} n^{4} \cdot (2 n^{3}))$

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 m^{3} n (3 + m^{3} \cdot (2 n^{4 + 3}))$

Step 2.5

Add $4$ and $3$ .

$2 m^{3} n (3 + m^{3} \cdot (2 n^{7}))$

Step 3

Rewrite using the commutative property of multiplication.

$2 m^{3} n (3 + 2 m^{3} n^{7})$

Step 4

The greatest common factor $GCF$ is the term in front of the factored expression.

$2 m^{3} n$