Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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

Step 1.1.2

Combine $- 3$ and $\frac{1}{y}$ .

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

Step 1.1.3

Move the negative in front of the fraction.

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

Step 1.2

Simplify each term.

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Step 1.2.1

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

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

Step 1.2.2

Combine $3$ and $\frac{1}{x}$ .

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

Step 2

Expand $(2 x - \frac{3}{y}) (\frac{3}{x} + x y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Cancel the common factor of $x$ .

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Step 3.1.1.1

Factor $x$ out of $2 x$ .

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

Step 3.1.1.2

Cancel the common factor.

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

Step 3.1.1.3

Rewrite the expression.

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

Step 3.1.2

Multiply $2$ by $3$ .

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

Step 3.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1.3.1

Move $x$ .

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

Step 3.1.3.2

Multiply $x$ by $x$ .

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

Step 3.1.4

Multiply $- \frac{3}{y} \cdot \frac{3}{x}$ .

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Step 3.1.4.1

Multiply $\frac{3}{x}$ by $\frac{3}{y}$ .

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

Step 3.1.4.2

Multiply $3$ by $3$ .

$6 + 2 x^{2} y - \frac{9}{x y} - \frac{3}{y} (x y)$

Step 3.1.5

Cancel the common factor of $y$ .

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Step 3.1.5.1

Move the leading negative in $- \frac{3}{y}$ into the numerator.

$6 + 2 x^{2} y - \frac{9}{x y} + \frac{- 3}{y} (x y)$

Step 3.1.5.2

Factor $y$ out of $x y$ .

$6 + 2 x^{2} y - \frac{9}{x y} + \frac{- 3}{y} (y x)$

Step 3.1.5.3

Cancel the common factor.

$6 + 2 x^{2} y - \frac{9}{x y} + \frac{- 3}{y} (y x)$

Step 3.1.5.4

Rewrite the expression.

$6 + 2 x^{2} y - \frac{9}{x y} - 3 x$

Step 3.2

Reorder.

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Step 3.2.1

Move $- \frac{9}{x y}$ .

$6 + 2 x^{2} y - 3 x - \frac{9}{x y}$

Step 3.2.2

Move $6$ .

$2 x^{2} y - 3 x + 6 - \frac{9}{x y}$