Algebra Examples

$\frac{25 x y^{4} + 60 x y^{3}}{5 x y}$

Step 1

Factor $5 x y^{3}$ out of $25 x y^{4} + 60 x y^{3}$ .

Tap for more steps...

Step 1.1

Factor $5 x y^{3}$ out of $25 x y^{4}$ .

$\frac{5 x y^{3} (5 y) + 60 x y^{3}}{5 x y}$

Step 1.2

Factor $5 x y^{3}$ out of $60 x y^{3}$ .

$\frac{5 x y^{3} (5 y) + 5 x y^{3} (12)}{5 x y}$

Step 1.3

Factor $5 x y^{3}$ out of $5 x y^{3} (5 y) + 5 x y^{3} (12)$ .

$\frac{5 x y^{3} (5 y + 12)}{5 x y}$

Step 2

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

$\frac{5 x y^{3} (5 y + 12)}{5 x y}$

Step 2.2

Rewrite the expression.

$\frac{x y^{3} (5 y + 12)}{x y}$

Step 3

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{x y^{3} (5 y + 12)}{x y}$

Step 3.2

Rewrite the expression.

$\frac{y^{3} (5 y + 12)}{y}$

Step 4

Cancel the common factor of $y^{3}$ and $y$ .

Tap for more steps...

Step 4.1

Factor $y$ out of $y^{3} (5 y + 12)$ .

$\frac{y (y^{2} (5 y + 12))}{y}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

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

$\frac{y (y^{2} (5 y + 12))}{y^{1}}$

Step 4.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (y^{2} (5 y + 12))}{y \cdot 1}$

Step 4.2.3

Cancel the common factor.

$\frac{y (y^{2} (5 y + 12))}{y \cdot 1}$

Step 4.2.4

Rewrite the expression.

$\frac{y^{2} (5 y + 12)}{1}$

Step 4.2.5

Divide $y^{2} (5 y + 12)$ by $1$ .

$y^{2} (5 y + 12)$

Step 5

Apply the distributive property.

$y^{2} (5 y) + y^{2} \cdot 12$

Step 6

Rewrite using the commutative property of multiplication.

$5 y^{2} y + y^{2} \cdot 12$

Step 7

Move $12$ to the left of $y^{2}$ .

$5 y^{2} y + 12 \cdot y^{2}$

Step 8

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

Tap for more steps...

Step 8.1

Move $y$ .

$5 (y \cdot y^{2}) + 12 \cdot y^{2}$

Step 8.2

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

Tap for more steps...

Step 8.2.1

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

$5 (y^{1} y^{2}) + 12 \cdot y^{2}$

Step 8.2.2

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

$5 y^{1 + 2} + 12 \cdot y^{2}$

Step 8.3

Add $1$ and $2$ .

$5 y^{3} + 12 \cdot y^{2}$

$5 y^{3} + 12 y^{2}$