Precalculus Examples

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Combine $x$ and $\frac{1}{y^{2}}$ .

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

Step 3

Multiply $\frac{x}{y^{2}}$ by $x y^{2} - 3 y^{3}$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

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

$x (x - 3 y)$

Step 6

Apply the distributive property.

$x \cdot x + x (- 3 y)$

Step 7

Simplify the expression.

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Step 7.1

Multiply $x$ by $x$ .

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

Step 7.2

Rewrite using the commutative property of multiplication.

$x^{2} - 3 x y$