Algebra Examples

$81 x^{4} = 3 x$

Step 1

Subtract $3 x$ from both sides of the equation.

$81 x^{4} - 3 x = 0$

Step 2

Factor the left side.

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Step 2.1

Factor $3 x$ out of $81 x^{4} - 3 x$ .

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Step 2.1.1

Factor $3 x$ out of $81 x^{4}$ .

$3 x (27 x^{3}) - 3 x = 0$

Step 2.1.2

Factor $3 x$ out of $- 3 x$ .

$3 x (27 x^{3}) + 3 x (- 1) = 0$

Step 2.1.3

Factor $3 x$ out of $3 x (27 x^{3}) + 3 x (- 1)$ .

$3 x (27 x^{3} - 1) = 0$

Step 2.2

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

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

Step 2.3

Rewrite $1$ as $1^{3}$ .

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

Step 2.4

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 $a = 3 x$ and $b = 1$ .

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

Step 2.5

Factor.

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Step 2.5.1

Simplify.

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Step 2.5.1.1

Apply the product rule to $3 x$ .

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

Step 2.5.1.2

Raise $3$ to the power of $2$ .

$3 x ((3 x - 1) (9 x^{2} + 3 x \cdot 1 + 1^{2})) = 0$

Step 2.5.1.3

Multiply $3$ by $1$ .

$3 x ((3 x - 1) (9 x^{2} + 3 x + 1^{2})) = 0$

Step 2.5.1.4

One to any power is one.

$3 x ((3 x - 1) (9 x^{2} + 3 x + 1)) = 0$

Step 2.5.2

Remove unnecessary parentheses.

$3 x (3 x - 1) (9 x^{2} + 3 x + 1) = 0$