Algebra Examples

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

Step 1

Add $b x$ to both sides of the equation.

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

Step 2

Add $b^{3}$ to both sides of the equation.

$a x + b x = a^{3} + b^{3}$

Step 3

Factor $x$ out of $a x + b x$ .

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Step 3.1

Factor $x$ out of $a x$ .

$x a + b x = a^{3} + b^{3}$

Step 3.2

Factor $x$ out of $b x$ .

$x a + x b = a^{3} + b^{3}$

Step 3.3

Factor $x$ out of $x a + x b$ .

$x (a + b) = a^{3} + b^{3}$

Step 4

Divide each term in $x (a + b) = a^{3} + b^{3}$ by $a + b$ and simplify.

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Step 4.1

Divide each term in $x (a + b) = a^{3} + b^{3}$ by $a + b$ .

$\frac{x (a + b)}{a + b} = \frac{a^{3}}{a + b} + \frac{b^{3}}{a + b}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $a + b$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x (a + b)}{a + b} = \frac{a^{3}}{a + b} + \frac{b^{3}}{a + b}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{a^{3}}{a + b} + \frac{b^{3}}{a + b}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$x = \frac{a^{3} + b^{3}}{a + b}$

Step 4.3.2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = a$ and $b = b$ .

$x = \frac{(a + b) (a^{2} - a b + b^{2})}{a + b}$

Step 4.3.3

Cancel the common factor of $a + b$ .

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Step 4.3.3.1

Cancel the common factor.

$x = \frac{(a + b) (a^{2} - a b + b^{2})}{a + b}$

Step 4.3.3.2

Divide $a^{2} - a b + b^{2}$ by $1$ .

$x = a^{2} - a b + b^{2}$