Basic Math Examples

$2 w^{2} (w - 6) + (w - 6)$

Step 1

Remove parentheses.

$2 w^{2} (w - 6) + w - 6$

Step 2

Apply the distributive property.

$2 w^{2} w + 2 w^{2} \cdot - 6 + w - 6$

Step 3

Multiply

$w^{2}$ by

$w$ by adding the exponents.

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Step 3.1

Move

$w$ .

$2 (w \cdot w^{2}) + 2 w^{2} \cdot - 6 + w - 6$

Step 3.2

Multiply

$w$ by

$w^{2}$ .

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Step 3.2.1

Raise

$w$ to the power of

$1$ .

$2 (w^{1} w^{2}) + 2 w^{2} \cdot - 6 + w - 6$

Step 3.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 w^{1 + 2} + 2 w^{2} \cdot - 6 + w - 6$

Step 3.3

Add

$1$ and

$2$ .

$2 w^{3} + 2 w^{2} \cdot - 6 + w - 6$

Step 4

Multiply

$- 6$ by

$2$ .

$2 w^{3} - 12 w^{2} + w - 6$

Step 5

Rewrite

$2 w^{3} - 12 w^{2} + w - 6$ 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.

$(2 w^{3} - 12 w^{2}) + w - 6$

Step 5.1.2

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

$2 w^{2} (w - 6) + 1 (w - 6)$

Step 5.2

Factor the polynomial by factoring out the greatest common factor,

$w - 6$ .

$(w - 6) (2 w^{2} + 1)$