Divide (-25x^4y^3+30x^2y^5)/(-5x^2y)

$\frac{- 25 x^{4} y^{3} + 30 x^{2} y^{5}}{- 5 x^{2} y}$

Step 1

Factor $5 x^{2} y^{3}$ out of $- 25 x^{4} y^{3} + 30 x^{2} y^{5}$ .

Factor $5 x^{2} y^{3}$ out of $- 25 x^{4} y^{3}$ .

$\frac{5 x^{2} y^{3} (- 5 x^{2}) + 30 x^{2} y^{5}}{- 5 x^{2} y}$

Factor $5 x^{2} y^{3}$ out of $30 x^{2} y^{5}$ .

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

Factor $5 x^{2} y^{3}$ out of $5 x^{2} y^{3} (- 5 x^{2}) + 5 x^{2} y^{3} (6 y^{2})$ .

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

Step 2

Cancel the common factor of $5$ and $- 5$ .

Factor $5$ out of $5 x^{2} y^{3} (- 5 x^{2} + 6 y^{2})$ .

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

Cancel the common factors.

Factor $5$ out of $- 5 x^{2} y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

Factor $y$ out of $y^{3} (- 5 x^{2} + 6 y^{2})$ .

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

Move the negative one from the denominator of $\frac{y^{2} (- 5 x^{2} + 6 y^{2})}{- 1}$ .

$- 1 \cdot (y^{2} (- 5 x^{2} + 6 y^{2}))$

Step 5

Rewrite $- 1 \cdot (y^{2} (- 5 x^{2} + 6 y^{2}))$ as $- (y^{2} (- 5 x^{2} + 6 y^{2}))$ .

$- (y^{2} (- 5 x^{2} + 6 y^{2}))$

Step 6

Apply the distributive property.

$- (y^{2} (- 5 x^{2}) + y^{2} (6 y^{2}))$

Step 7

Rewrite using the commutative property of multiplication.

$- (- 5 y^{2} x^{2} + y^{2} (6 y^{2}))$

Step 8

Rewrite using the commutative property of multiplication.

$- (- 5 y^{2} x^{2} + 6 y^{2} y^{2})$

Step 9

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

Move $y^{2}$ .

$- (- 5 y^{2} x^{2} + 6 (y^{2} y^{2}))$

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

$- (- 5 y^{2} x^{2} + 6 y^{2 + 2})$

Add $2$ and $2$ .

$- (- 5 y^{2} x^{2} + 6 y^{4})$

Step 10

Apply the distributive property.

$- (- 5 y^{2} x^{2}) - (6 y^{4})$

Step 11

Multiply $- 5$ by $- 1$ .

$5 (y^{2} x^{2}) - (6 y^{4})$

Step 12

Multiply $6$ by $- 1$ .

$5 y^{2} x^{2} - 6 y^{4}$

Divide (-25x^4y^3+30x^2y^5)/(-5x^2y)

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