Algebra Examples

$12 x^{5} + 8 x^{3} = 2 x^{3} (6 x^{2} + 4)$

Step 1

Subtract $2 x^{3} (6 x^{2} + 4)$ from both sides of the equation.

$12 x^{5} + 8 x^{3} - 2 x^{3} (6 x^{2} + 4) = 0$

Step 2

Simplify $12 x^{5} + 8 x^{3} - 2 x^{3} (6 x^{2} + 4)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$12 x^{5} + 8 x^{3} - 2 x^{3} (6 x^{2}) - 2 x^{3} \cdot 4 = 0$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$12 x^{5} + 8 x^{3} - 2 \cdot 6 x^{3} x^{2} - 2 x^{3} \cdot 4 = 0$

Step 2.1.3

Multiply $4$ by $- 2$ .

$12 x^{5} + 8 x^{3} - 2 \cdot 6 x^{3} x^{2} - 8 x^{3} = 0$

Step 2.1.4

Simplify each term.

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Step 2.1.4.1

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 2.1.4.1.1

Move $x^{2}$ .

$12 x^{5} + 8 x^{3} - 2 \cdot 6 (x^{2} x^{3}) - 8 x^{3} = 0$

Step 2.1.4.1.2

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

$12 x^{5} + 8 x^{3} - 2 \cdot 6 x^{2 + 3} - 8 x^{3} = 0$

Step 2.1.4.1.3

Add $2$ and $3$ .

$12 x^{5} + 8 x^{3} - 2 \cdot 6 x^{5} - 8 x^{3} = 0$

Step 2.1.4.2

Multiply $- 2$ by $6$ .

$12 x^{5} + 8 x^{3} - 12 x^{5} - 8 x^{3} = 0$

Step 2.2

Combine the opposite terms in $12 x^{5} + 8 x^{3} - 12 x^{5} - 8 x^{3}$ .

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Step 2.2.1

Subtract $12 x^{5}$ from $12 x^{5}$ .

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

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 $8 x^{3}$ .

$0 = 0$

Step 3

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

Always true