Algebra Examples

$12 m^{2} n + 24 m^{3} \cdot 3 n^{2} - 36 m^{4} n^{3}$

Step 1

Remove parentheses.

$12 m^{2} n + 24 m^{3} \cdot 3 n^{2} - 36 m^{4} n^{3}$

Step 2

Factor $- 12 m^{2} n$ out of $12 m^{2} n + 24 m^{3} \cdot 3 n^{2} - 36 m^{4} n^{3}$ .

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Step 2.1

Reorder the expression.

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Step 2.1.1

Move $m^{3}$ .

$12 m^{2} n + 24 \cdot 3 m^{3} n^{2} - 36 m^{4} n^{3}$

Step 2.1.2

Move $12 m^{2} n$ .

$24 \cdot 3 m^{3} n^{2} - 36 m^{4} n^{3} + 12 m^{2} n$

Step 2.1.3

Reorder $24 \cdot 3 m^{3} n^{2}$ and $- 36 m^{4} n^{3}$ .

$- 36 m^{4} n^{3} + 24 \cdot 3 m^{3} n^{2} + 12 m^{2} n$

Step 2.2

Factor $- 12 m^{2} n$ out of $- 36 m^{4} n^{3}$ .

$- 12 m^{2} n (3 m^{2} n^{2}) + 24 \cdot 3 m^{3} n^{2} + 12 m^{2} n$

Step 2.3

Factor $- 12 m^{2} n$ out of $24 \cdot 3 m^{3} n^{2}$ .

$- 12 m^{2} n (3 m^{2} n^{2}) - 12 m^{2} n (- 2 \cdot 3 m n) + 12 m^{2} n$

Step 2.4

Factor $- 12 m^{2} n$ out of $12 m^{2} n$ .

$- 12 m^{2} n (3 m^{2} n^{2}) - 12 m^{2} n (- 2 \cdot 3 m n) - 12 m^{2} n (- 1)$

Step 2.5

Factor $- 12 m^{2} n$ out of $- 12 m^{2} n (3 m^{2} n^{2}) - 12 m^{2} n (- 2 \cdot 3 m n)$ .

$- 12 m^{2} n (3 m^{2} n^{2} - 2 \cdot 3 m n) - 12 m^{2} n (- 1)$

Step 2.6

Factor $- 12 m^{2} n$ out of $- 12 m^{2} n (3 m^{2} n^{2} - 2 \cdot 3 m n) - 12 m^{2} n (- 1)$ .

$- 12 m^{2} n (3 m^{2} n^{2} - 2 \cdot 3 m n - 1)$

Step 3

Multiply $- 2$ by $3$ .

$- 12 m^{2} n (3 m^{2} n^{2} - 6 m n - 1)$