Pre-Algebra Examples

$\frac{12 w^{4} - 6 w^{3} + w^{2}}{3 w^{2}}$

Step 1

Factor $w^{2}$ out of $12 w^{4} - 6 w^{3} + w^{2}$ .

Tap for more steps...

Step 1.1

Factor $w^{2}$ out of $12 w^{4}$ .

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

Step 1.2

Factor $w^{2}$ out of $- 6 w^{3}$ .

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

Step 1.3

Multiply by $1$ .

$\frac{w^{2} (12 w^{2}) + w^{2} (- 6 w) + w^{2} \cdot 1}{3 w^{2}}$

Step 1.4

Factor $w^{2}$ out of $w^{2} (12 w^{2}) + w^{2} (- 6 w)$ .

$\frac{w^{2} (12 w^{2} - 6 w) + w^{2} \cdot 1}{3 w^{2}}$

Step 1.5

Factor $w^{2}$ out of $w^{2} (12 w^{2} - 6 w) + w^{2} \cdot 1$ .

$\frac{w^{2} (12 w^{2} - 6 w + 1)}{3 w^{2}}$

Step 2

Cancel the common factor of $w^{2}$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

$\frac{w^{2} (12 w^{2} - 6 w + 1)}{3 w^{2}}$

Step 2.2

Rewrite the expression.

$\frac{12 w^{2} - 6 w + 1}{3}$

Step 3

Split the fraction $\frac{12 w^{2} - 6 w + 1}{3}$ into two fractions.

$\frac{12 w^{2} - 6 w}{3} + \frac{1}{3}$

Step 4

Split the fraction $\frac{12 w^{2} - 6 w}{3}$ into two fractions.

$\frac{12 w^{2}}{3} + \frac{- 6 w}{3} + \frac{1}{3}$

Step 5

Cancel the common factor of $12$ and $3$ .

Tap for more steps...

Step 5.1

Factor $3$ out of $12 w^{2}$ .

$\frac{3 (4 w^{2})}{3} + \frac{- 6 w}{3} + \frac{1}{3}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $3$ out of $3$ .

$\frac{3 (4 w^{2})}{3 (1)} + \frac{- 6 w}{3} + \frac{1}{3}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (4 w^{2})}{3 \cdot 1} + \frac{- 6 w}{3} + \frac{1}{3}$

Step 5.2.3

Rewrite the expression.

$\frac{4 w^{2}}{1} + \frac{- 6 w}{3} + \frac{1}{3}$

Step 5.2.4

Divide $4 w^{2}$ by $1$ .

$4 w^{2} + \frac{- 6 w}{3} + \frac{1}{3}$

Step 6

Cancel the common factor of $- 6$ and $3$ .

Tap for more steps...

Step 6.1

Factor $3$ out of $- 6 w$ .

$4 w^{2} + \frac{3 (- 2 w)}{3} + \frac{1}{3}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $3$ out of $3$ .

$4 w^{2} + \frac{3 (- 2 w)}{3 (1)} + \frac{1}{3}$

Step 6.2.2

Cancel the common factor.

$4 w^{2} + \frac{3 (- 2 w)}{3 \cdot 1} + \frac{1}{3}$

Step 6.2.3

Rewrite the expression.

$4 w^{2} + \frac{- 2 w}{1} + \frac{1}{3}$

Step 6.2.4

Divide $- 2 w$ by $1$ .

$4 w^{2} - 2 w + \frac{1}{3}$