Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Combine $5$ and $\frac{x + 1}{x}$ .

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Factor $x$ out of $x^{3}$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$5 (x + 1) x^{2}$

Step 4

Apply the distributive property.

$(5 x + 5 \cdot 1) x^{2}$

Step 5

Multiply $5$ by $1$ .

$(5 x + 5) x^{2}$

Step 6

Apply the distributive property.

$5 x \cdot x^{2} + 5 x^{2}$

Step 7

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 7.1

Move $x^{2}$ .

$5 (x^{2} x) + 5 x^{2}$

Step 7.2

Multiply $x^{2}$ by $x$ .

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Step 7.2.1

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

$5 (x^{2} x^{1}) + 5 x^{2}$

Step 7.2.2

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

$5 x^{2 + 1} + 5 x^{2}$

Step 7.3

Add $2$ and $1$ .

$5 x^{3} + 5 x^{2}$