Algebra Examples

$(\frac{5}{3} x + 4) (\frac{1}{3} x + 1)$

Step 1

Combine fractions.

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Step 1.1

Combine $\frac{5}{3}$ and $x$ .

$(\frac{5 x}{3} + 4) (\frac{1}{3} x + 1)$

Step 1.2

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

$(\frac{5 x}{3} + 4) (\frac{x}{3} + 1)$

Step 2

Expand $(\frac{5 x}{3} + 4) (\frac{x}{3} + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\frac{5 x}{3} (\frac{x}{3} + 1) + 4 (\frac{x}{3} + 1)$

Step 2.2

Apply the distributive property.

$\frac{5 x}{3} \cdot \frac{x}{3} + \frac{5 x}{3} \cdot 1 + 4 (\frac{x}{3} + 1)$

Step 2.3

Apply the distributive property.

$\frac{5 x}{3} \cdot \frac{x}{3} + \frac{5 x}{3} \cdot 1 + 4 \frac{x}{3} + 4 \cdot 1$

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

Multiply $\frac{5 x}{3} \cdot \frac{x}{3}$ .

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Step 3.1.1.1

Multiply $\frac{5 x}{3}$ by $\frac{x}{3}$ .

$\frac{5 x \cdot x}{3 \cdot 3} + \frac{5 x}{3} \cdot 1 + 4 \frac{x}{3} + 4 \cdot 1$

Step 3.1.1.2

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

$\frac{5 (x^{1} x)}{3 \cdot 3} + \frac{5 x}{3} \cdot 1 + 4 \frac{x}{3} + 4 \cdot 1$

Step 3.1.1.3

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

$\frac{5 (x^{1} x^{1})}{3 \cdot 3} + \frac{5 x}{3} \cdot 1 + 4 \frac{x}{3} + 4 \cdot 1$

Step 3.1.1.4

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

$\frac{5 x^{1 + 1}}{3 \cdot 3} + \frac{5 x}{3} \cdot 1 + 4 \frac{x}{3} + 4 \cdot 1$

Step 3.1.1.5

Add $1$ and $1$ .

$\frac{5 x^{2}}{3 \cdot 3} + \frac{5 x}{3} \cdot 1 + 4 \frac{x}{3} + 4 \cdot 1$

Step 3.1.1.6

Multiply $3$ by $3$ .

$\frac{5 x^{2}}{9} + \frac{5 x}{3} \cdot 1 + 4 \frac{x}{3} + 4 \cdot 1$

Step 3.1.2

Multiply $\frac{5 x}{3}$ by $1$ .

$\frac{5 x^{2}}{9} + \frac{5 x}{3} + 4 \frac{x}{3} + 4 \cdot 1$

Step 3.1.3

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

$\frac{5 x^{2}}{9} + \frac{5 x}{3} + \frac{4 x}{3} + 4 \cdot 1$

Step 3.1.4

Multiply $4$ by $1$ .

$\frac{5 x^{2}}{9} + \frac{5 x}{3} + \frac{4 x}{3} + 4$

Step 3.2

Combine the numerators over the common denominator.

$\frac{5 x^{2}}{9} + \frac{5 x + 4 x}{3} + 4$

Step 4

Add $5 x$ and $4 x$ .

$\frac{5 x^{2}}{9} + \frac{9 x}{3} + 4$

Step 5

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

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Step 5.1

Factor $3$ out of $9 x$ .

$\frac{5 x^{2}}{9} + \frac{3 (3 x)}{3} + 4$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $3$ .

$\frac{5 x^{2}}{9} + \frac{3 (3 x)}{3 (1)} + 4$

Step 5.2.2

Cancel the common factor.

$\frac{5 x^{2}}{9} + \frac{3 (3 x)}{3 \cdot 1} + 4$

Step 5.2.3

Rewrite the expression.

$\frac{5 x^{2}}{9} + \frac{3 x}{1} + 4$

Step 5.2.4

Divide $3 x$ by $1$ .

$\frac{5 x^{2}}{9} + 3 x + 4$