Algebra Examples

$x^{3} + y^{9} = 8$

Step 1

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

$y^{9} = 8 - x^{3}$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \sqrt[9]{8 - x^{3}}$

Step 3

Simplify $\sqrt[9]{8 - x^{3}}$ .

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Step 3.1

Rewrite $8$ as $2^{3}$ .

$y = \sqrt[9]{2^{3} - x^{3}}$

Step 3.2

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

$y = \sqrt[9]{(2 - x) (2^{2} + 2 x + x^{2})}$

Step 3.3

Raise $2$ to the power of $2$ .

$y = \sqrt[9]{(2 - x) (4 + 2 x + x^{2})}$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \sqrt[9]{(2 - x) (4 + 2 x + x^{2})}$