Algebra Examples

$18 x^{4} - 12 x^{2} = 6 x (3 x^{3} - 2 x)$

Step 1

Subtract $6 x (3 x^{3} - 2 x)$ from both sides of the equation.

$18 x^{4} - 12 x^{2} - 6 x (3 x^{3} - 2 x) = 0$

Step 2

Simplify $18 x^{4} - 12 x^{2} - 6 x (3 x^{3} - 2 x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$18 x^{4} - 12 x^{2} - 6 x (3 x^{3}) - 6 x (- 2 x) = 0$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$18 x^{4} - 12 x^{2} - 6 \cdot 3 x \cdot x^{3} - 6 x (- 2 x) = 0$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$18 x^{4} - 12 x^{2} - 6 \cdot 3 x \cdot x^{3} - 6 \cdot - 2 x \cdot x = 0$

Step 2.1.4

Simplify each term.

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Step 2.1.4.1

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 2.1.4.1.1

Move $x^{3}$ .

$18 x^{4} - 12 x^{2} - 6 \cdot 3 (x^{3} x) - 6 \cdot - 2 x \cdot x = 0$

Step 2.1.4.1.2

Multiply $x^{3}$ by $x$ .

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Step 2.1.4.1.2.1

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

$18 x^{4} - 12 x^{2} - 6 \cdot 3 (x^{3} x^{1}) - 6 \cdot - 2 x \cdot x = 0$

Step 2.1.4.1.2.2

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

$18 x^{4} - 12 x^{2} - 6 \cdot 3 x^{3 + 1} - 6 \cdot - 2 x \cdot x = 0$

Step 2.1.4.1.3

Add $3$ and $1$ .

$18 x^{4} - 12 x^{2} - 6 \cdot 3 x^{4} - 6 \cdot - 2 x \cdot x = 0$

Step 2.1.4.2

Multiply $- 6$ by $3$ .

$18 x^{4} - 12 x^{2} - 18 x^{4} - 6 \cdot - 2 x \cdot x = 0$

Step 2.1.4.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.4.3.1

Move $x$ .

$18 x^{4} - 12 x^{2} - 18 x^{4} - 6 \cdot - 2 (x \cdot x) = 0$

Step 2.1.4.3.2

Multiply $x$ by $x$ .

$18 x^{4} - 12 x^{2} - 18 x^{4} - 6 \cdot - 2 x^{2} = 0$

Step 2.1.4.4

Multiply $- 6$ by $- 2$ .

$18 x^{4} - 12 x^{2} - 18 x^{4} + 12 x^{2} = 0$

Step 2.2

Combine the opposite terms in $18 x^{4} - 12 x^{2} - 18 x^{4} + 12 x^{2}$ .

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Step 2.2.1

Subtract $18 x^{4}$ from $18 x^{4}$ .

$- 12 x^{2} + 0 + 12 x^{2} = 0$

Step 2.2.2

Add $- 12 x^{2}$ and $0$ .

$- 12 x^{2} + 12 x^{2} = 0$

Step 2.2.3

Add $- 12 x^{2}$ and $12 x^{2}$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true