Algebra Examples

$x^{9} + 8 x^{3} = {(x^{3})}^{3} + {(2 x)}^{3}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

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

$x^{9} + 8 x^{3} - {(x^{3})}^{3} = {(2 x)}^{3}$

Step 1.2

Subtract ${(2 x)}^{3}$ from both sides of the equation.

$x^{9} + 8 x^{3} - {(x^{3})}^{3} - {(2 x)}^{3} = 0$

Step 2

Simplify $x^{9} + 8 x^{3} - {(x^{3})}^{3} - {(2 x)}^{3}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply the exponents in ${(x^{3})}^{3}$ .

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Step 2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{9} + 8 x^{3} - x^{3 \cdot 3} - {(2 x)}^{3} = 0$

Step 2.1.1.2

Multiply $3$ by $3$ .

$x^{9} + 8 x^{3} - x^{9} - {(2 x)}^{3} = 0$

Step 2.1.2

Apply the product rule to $2 x$ .

$x^{9} + 8 x^{3} - x^{9} - (2^{3} x^{3}) = 0$

Step 2.1.3

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

$x^{9} + 8 x^{3} - x^{9} - (8 x^{3}) = 0$

Step 2.1.4

Multiply $8$ by $- 1$ .

$x^{9} + 8 x^{3} - x^{9} - 8 x^{3} = 0$

Step 2.2

Combine the opposite terms in $x^{9} + 8 x^{3} - x^{9} - 8 x^{3}$ .

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Step 2.2.1

Subtract $x^{9}$ from $x^{9}$ .

$8 x^{3} + 0 - 8 x^{3} = 0$

Step 2.2.2

Add $8 x^{3}$ and $0$ .

$8 x^{3} - 8 x^{3} = 0$

Step 2.2.3

Subtract $8 x^{3}$ from $8 x^{3}$ .

$0 = 0$