Algebra Examples

$(5 a + 3 b) (4 a^{- 1} - 2 b^{- 1})$

Step 1

Simplify each term.

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Step 1.1

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

$(5 a + 3 b) (4 \frac{1}{a} - 2 b^{- 1})$

Step 1.2

Combine $4$ and $\frac{1}{a}$ .

$(5 a + 3 b) (\frac{4}{a} - 2 b^{- 1})$

Step 1.3

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

$(5 a + 3 b) (\frac{4}{a} - 2 \frac{1}{b})$

Step 1.4

Combine $- 2$ and $\frac{1}{b}$ .

$(5 a + 3 b) (\frac{4}{a} + \frac{- 2}{b})$

Step 1.5

Move the negative in front of the fraction.

$(5 a + 3 b) (\frac{4}{a} - \frac{2}{b})$

Step 2

Expand $(5 a + 3 b) (\frac{4}{a} - \frac{2}{b})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 a (\frac{4}{a} - \frac{2}{b}) + 3 b (\frac{4}{a} - \frac{2}{b})$

Step 2.2

Apply the distributive property.

$5 a \frac{4}{a} + 5 a (- \frac{2}{b}) + 3 b (\frac{4}{a} - \frac{2}{b})$

Step 2.3

Apply the distributive property.

$5 a \frac{4}{a} + 5 a (- \frac{2}{b}) + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Cancel the common factor of $a$ .

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Step 3.1.1.1

Factor $a$ out of $5 a$ .

$a \cdot 5 \frac{4}{a} + 5 a (- \frac{2}{b}) + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.1.2

Cancel the common factor.

$a \cdot 5 \frac{4}{a} + 5 a (- \frac{2}{b}) + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.1.3

Rewrite the expression.

$5 \cdot 4 + 5 a (- \frac{2}{b}) + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.2

Multiply $5$ by $4$ .

$20 + 5 a (- \frac{2}{b}) + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.3

Multiply $5 a (- \frac{2}{b})$ .

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Step 3.1.3.1

Multiply $- 1$ by $5$ .

$20 - 5 a \frac{2}{b} + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.3.2

Combine $- 5$ and $\frac{2}{b}$ .

$20 + a \frac{- 5 \cdot 2}{b} + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.3.3

Multiply $- 5$ by $2$ .

$20 + a \frac{- 10}{b} + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.3.4

Combine $a$ and $\frac{- 10}{b}$ .

$20 + \frac{a \cdot - 10}{b} + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.4

Move $- 10$ to the left of $a$ .

$20 + \frac{- 10 \cdot a}{b} + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.5

Move the negative in front of the fraction.

$20 - \frac{10 \cdot a}{b} + 3 b \frac{4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.6

Multiply $3 b \frac{4}{a}$ .

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Step 3.1.6.1

Combine $3$ and $\frac{4}{a}$ .

$20 - \frac{10 a}{b} + b \frac{3 \cdot 4}{a} + 3 b (- \frac{2}{b})$

Step 3.1.6.2

Multiply $3$ by $4$ .

$20 - \frac{10 a}{b} + b \frac{12}{a} + 3 b (- \frac{2}{b})$

Step 3.1.6.3

Combine $b$ and $\frac{12}{a}$ .

$20 - \frac{10 a}{b} + \frac{b \cdot 12}{a} + 3 b (- \frac{2}{b})$

Step 3.1.7

Move $12$ to the left of $b$ .

$20 - \frac{10 a}{b} + \frac{12 \cdot b}{a} + 3 b (- \frac{2}{b})$

Step 3.1.8

Cancel the common factor of $b$ .

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Step 3.1.8.1

Move the leading negative in $- \frac{2}{b}$ into the numerator.

$20 - \frac{10 a}{b} + \frac{12 b}{a} + 3 b \frac{- 2}{b}$

Step 3.1.8.2

Factor $b$ out of $3 b$ .

$20 - \frac{10 a}{b} + \frac{12 b}{a} + b \cdot 3 \frac{- 2}{b}$

Step 3.1.8.3

Cancel the common factor.

$20 - \frac{10 a}{b} + \frac{12 b}{a} + b \cdot 3 \frac{- 2}{b}$

Step 3.1.8.4

Rewrite the expression.

$20 - \frac{10 a}{b} + \frac{12 b}{a} + 3 \cdot - 2$

Step 3.1.9

Multiply $3$ by $- 2$ .

$20 - \frac{10 a}{b} + \frac{12 b}{a} - 6$

Step 3.2

Subtract $6$ from $20$ .

$14 - \frac{10 a}{b} + \frac{12 b}{a}$

Step 4

Move $14$ .

$- \frac{10 a}{b} + \frac{12 b}{a} + 14$