Algebra Examples

$\frac{1}{7} x^{2} (x - 7)$

Step 1

Apply the distributive property.

$\frac{1}{7} \cdot (x^{2} x + x^{2} \cdot - 7)$

Step 2

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

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Step 2.1

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

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Step 2.1.1

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

$\frac{1}{7} \cdot (x^{2} x^{1} + x^{2} \cdot - 7)$

Step 2.1.2

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

$\frac{1}{7} \cdot (x^{2 + 1} + x^{2} \cdot - 7)$

Step 2.2

Add $2$ and $1$ .

$\frac{1}{7} \cdot (x^{3} + x^{2} \cdot - 7)$

Step 3

Move $- 7$ to the left of $x^{2}$ .

$\frac{1}{7} \cdot (x^{3} - 7 \cdot x^{2})$

Step 4

Apply the distributive property.

$\frac{1}{7} x^{3} + \frac{1}{7} (- 7 x^{2})$

Step 5

Combine $\frac{1}{7}$ and $x^{3}$ .

$\frac{x^{3}}{7} + \frac{1}{7} (- 7 x^{2})$

Step 6

Cancel the common factor of $7$ .

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Step 6.1

Factor $7$ out of $- 7 x^{2}$ .

$\frac{x^{3}}{7} + \frac{1}{7} (7 (- x^{2}))$

Step 6.2

Cancel the common factor.

$\frac{x^{3}}{7} + \frac{1}{7} (7 (- x^{2}))$

Step 6.3

Rewrite the expression.

$\frac{x^{3}}{7} - x^{2}$