Algebra Examples

$\frac{- 9 y^{2}}{5 x} \cdot \frac{- 10 x^{2}}{3 y}$

Step 1

Combine.

$\frac{- 9 y^{2} (- 10 x^{2})}{5 x (3 y)}$

Step 2

Cancel the common factor of $- 9$ and $3$ .

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Step 2.1

Factor $3$ out of $- 9 y^{2} (- 10 x^{2})$ .

$\frac{3 (- 3 y^{2} (- 10 x^{2}))}{5 x (3 y)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $5 x (3 y)$ .

$\frac{3 (- 3 y^{2} (- 10 x^{2}))}{3 (5 x (y))}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (- 3 y^{2} (- 10 x^{2}))}{3 (5 x (y))}$

Step 2.2.3

Rewrite the expression.

$\frac{- 3 y^{2} (- 10 x^{2})}{5 x (y)}$

$\frac{- 3 y^{2} (- 10 x^{2})}{5 x (y)}$

$\frac{- 3 y^{2} (- 10 x^{2})}{5 x (y)}$

Step 3

Cancel the common factor of $y^{2}$ and $y$ .

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Step 3.1

Factor $y$ out of $- 3 y^{2} (- 10 x^{2})$ .

$\frac{y (- 3 y (- 10 x^{2}))}{5 x (y)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y$ out of $5 x (y)$ .

$\frac{y (- 3 y (- 10 x^{2}))}{y (5 x)}$

Step 3.2.2

Cancel the common factor.

$\frac{y (- 3 y (- 10 x^{2}))}{y (5 x)}$

Step 3.2.3

Rewrite the expression.

$\frac{- 3 y (- 10 x^{2})}{5 x}$

$\frac{- 3 y (- 10 x^{2})}{5 x}$

$\frac{- 3 y (- 10 x^{2})}{5 x}$

Step 4

Cancel the common factor of $- 10$ and $5$ .

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Step 4.1

Factor $5$ out of $- 3 y (- 10 x^{2})$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $5 x$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

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

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Step 5.1

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

$\frac{x (- 3 y (- 2 x))}{x}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

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

$\frac{x (- 3 y (- 2 x))}{x \cdot 1}$

Step 5.2.3

Cancel the common factor.

$\frac{x (- 3 y (- 2 x))}{x \cdot 1}$

Step 5.2.4

Rewrite the expression.

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

Step 5.2.5

Divide $- 3 y (- 2 x)$ by $1$ .

$- 3 y (- 2 x)$

$- 3 y (- 2 x)$

$- 3 y (- 2 x)$

Step 6

Simplify the expression.

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Step 6.1

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 2 y x$

Step 6.2

Multiply $- 3$ by $- 2$ .

$6 y x$

$6 y x$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$