Algebra Examples

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

Step 1

Simplify $x (x^{2} - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + x (x^{2} - 1) = 3 + x^{3}$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

$x \cdot x^{2} + x \cdot - 1 = 3 + x^{3}$

Step 1.4

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

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Step 1.4.1

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

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Step 1.4.1.1

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

$x^{1} x^{2} + x \cdot - 1 = 3 + x^{3}$

Step 1.4.1.2

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

$x^{1 + 2} + x \cdot - 1 = 3 + x^{3}$

Step 1.4.2

Add $1$ and $2$ .

$x^{3} + x \cdot - 1 = 3 + x^{3}$

Step 1.5

Move $- 1$ to the left of $x$ .

$x^{3} - 1 \cdot x = 3 + x^{3}$

Step 1.6

Rewrite $- 1 x$ as $- x$ .

$x^{3} - x = 3 + x^{3}$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $x^{3}$ from both sides of the equation.

$x^{3} - x - x^{3} = 3$

Step 2.2

Combine the opposite terms in $x^{3} - x - x^{3}$ .

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Step 2.2.1

Subtract $x^{3}$ from $x^{3}$ .

$- x + 0 = 3$

Step 2.2.2

Add $- x$ and $0$ .

$- x = 3$

Step 3

Divide each term in $- x = 3$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $3$ by $- 1$ .

$x = - 3$