Algebra Examples

$18 y^{3} - 6 y = 3 y (6 y^{2} - 2)$

Step 1

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

$18 y^{3} - 6 y - 3 y (6 y^{2} - 2) = 0$

Step 2

Simplify $18 y^{3} - 6 y - 3 y (6 y^{2} - 2)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$18 y^{3} - 6 y - 3 y (6 y^{2}) - 3 y \cdot - 2 = 0$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$18 y^{3} - 6 y - 3 \cdot 6 y \cdot y^{2} - 3 y \cdot - 2 = 0$

Step 2.1.3

Multiply $- 2$ by $- 3$ .

$18 y^{3} - 6 y - 3 \cdot 6 y \cdot y^{2} + 6 y = 0$

Step 2.1.4

Simplify each term.

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Step 2.1.4.1

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 2.1.4.1.1

Move $y^{2}$ .

$18 y^{3} - 6 y - 3 \cdot 6 (y^{2} y) + 6 y = 0$

Step 2.1.4.1.2

Multiply $y^{2}$ by $y$ .

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Step 2.1.4.1.2.1

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

$18 y^{3} - 6 y - 3 \cdot 6 (y^{2} y^{1}) + 6 y = 0$

Step 2.1.4.1.2.2

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

$18 y^{3} - 6 y - 3 \cdot 6 y^{2 + 1} + 6 y = 0$

Step 2.1.4.1.3

Add $2$ and $1$ .

$18 y^{3} - 6 y - 3 \cdot 6 y^{3} + 6 y = 0$

Step 2.1.4.2

Multiply $- 3$ by $6$ .

$18 y^{3} - 6 y - 18 y^{3} + 6 y = 0$

Step 2.2

Combine the opposite terms in $18 y^{3} - 6 y - 18 y^{3} + 6 y$ .

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Step 2.2.1

Subtract $18 y^{3}$ from $18 y^{3}$ .

$- 6 y + 0 + 6 y = 0$

Step 2.2.2

Add $- 6 y$ and $0$ .

$- 6 y + 6 y = 0$

Step 2.2.3

Add $- 6 y$ and $6 y$ .

$0 = 0$

Step 3

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

Always true