Pre-Algebra Examples

$\frac{6 x^{3} y^{4} + 6 x^{5} y^{8} - 6 x^{6} y^{5}}{3 x^{3} y^{4}}$

Step 1

Factor $6 x^{3} y^{4}$ out of $6 x^{3} y^{4} + 6 x^{5} y^{8} - 6 x^{6} y^{5}$ .

Tap for more steps...

Step 1.1

Factor $6 x^{3} y^{4}$ out of $6 x^{3} y^{4}$ .

$\frac{6 x^{3} y^{4} (1) + 6 x^{5} y^{8} - 6 x^{6} y^{5}}{3 x^{3} y^{4}}$

Step 1.2

Factor $6 x^{3} y^{4}$ out of $6 x^{5} y^{8}$ .

$\frac{6 x^{3} y^{4} (1) + 6 x^{3} y^{4} (x^{2} y^{4}) - 6 x^{6} y^{5}}{3 x^{3} y^{4}}$

Step 1.3

Factor $6 x^{3} y^{4}$ out of $- 6 x^{6} y^{5}$ .

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

Step 1.4

Factor $6 x^{3} y^{4}$ out of $6 x^{3} y^{4} (1) + 6 x^{3} y^{4} (x^{2} y^{4})$ .

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

Step 1.5

Factor $6 x^{3} y^{4}$ out of $6 x^{3} y^{4} (1 + x^{2} y^{4}) + 6 x^{3} y^{4} (- x^{3} y)$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Factor $3$ out of $6 x^{3} y^{4} (1 + x^{2} y^{4} - x^{3} y)$ .

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

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $3$ out of $3 x^{3} y^{4}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{3}$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factor of $y^{4}$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $2 (1 + x^{2} y^{4} - x^{3} y)$ by $1$ .

$2 (1 + x^{2} y^{4} - x^{3} y)$

Step 5

Apply the distributive property.

$2 \cdot 1 + 2 (x^{2} y^{4}) + 2 (- x^{3} y)$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Multiply $2$ by $1$ .

$2 + 2 (x^{2} y^{4}) + 2 (- x^{3} y)$

Step 6.2

Multiply $- 1$ by $2$ .

$2 + 2 x^{2} y^{4} - 2 (x^{3} y)$

$2 + 2 x^{2} y^{4} - 2 x^{3} y$