Basic Math Examples

$3 m^{2} (m - 2) + (m - 2)$

Step 1

Remove parentheses.

$3 m^{2} (m - 2) + m - 2$

Step 2

Apply the distributive property.

$3 m^{2} m + 3 m^{2} \cdot - 2 + m - 2$

Step 3

Multiply $m^{2}$ by $m$ by adding the exponents.

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Step 3.1

Move $m$ .

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

Step 3.2

Multiply $m$ by $m^{2}$ .

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Step 3.2.1

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

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

Step 3.2.2

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

$3 m^{1 + 2} + 3 m^{2} \cdot - 2 + m - 2$

Step 3.3

Add $1$ and $2$ .

$3 m^{3} + 3 m^{2} \cdot - 2 + m - 2$

Step 4

Multiply $- 2$ by $3$ .

$3 m^{3} - 6 m^{2} + m - 2$

Step 5

Rewrite $3 m^{3} - 6 m^{2} + m - 2$ in a factored form.

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Step 5.1

Factor out the greatest common factor from each group.

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Step 5.1.1

Group the first two terms and the last two terms.

$(3 m^{3} - 6 m^{2}) + m - 2$

Step 5.1.2

Factor out the greatest common factor (GCF) from each group.

$3 m^{2} (m - 2) + 1 (m - 2)$

Step 5.2

Factor the polynomial by factoring out the greatest common factor, $m - 2$ .

$(m - 2) (3 m^{2} + 1)$