Algebra Examples

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

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Simplify.

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Step 1.1.2.1

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

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Step 1.1.2.1.1

Move $x^{2}$ .

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

Step 1.1.2.1.2

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

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Step 1.1.2.1.2.1

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

$6 (x^{2} x^{1}) + 6 x (4 x) + 6 x \cdot - 2 - 2 x (3 x^{2} + 8) = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.2.1.2.2

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

$6 x^{2 + 1} + 6 x (4 x) + 6 x \cdot - 2 - 2 x (3 x^{2} + 8) = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.2.1.3

Add $2$ and $1$ .

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

Step 1.1.2.2

Rewrite using the commutative property of multiplication.

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

Step 1.1.2.3

Multiply $- 2$ by $6$ .

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

Step 1.1.3

Simplify each term.

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Step 1.1.3.1

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

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Step 1.1.3.1.1

Move $x$ .

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

Step 1.1.3.1.2

Multiply $x$ by $x$ .

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

Step 1.1.3.2

Multiply $6$ by $4$ .

$6 x^{3} + 24 x^{2} - 12 x - 2 x (3 x^{2} + 8) = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.4

Apply the distributive property.

$6 x^{3} + 24 x^{2} - 12 x - 2 x (3 x^{2}) - 2 x \cdot 8 = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.5

Rewrite using the commutative property of multiplication.

$6 x^{3} + 24 x^{2} - 12 x - 2 \cdot 3 x \cdot x^{2} - 2 x \cdot 8 = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.6

Multiply $8$ by $- 2$ .

$6 x^{3} + 24 x^{2} - 12 x - 2 \cdot 3 x \cdot x^{2} - 16 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.7

Simplify each term.

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Step 1.1.7.1

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

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Step 1.1.7.1.1

Move $x^{2}$ .

$6 x^{3} + 24 x^{2} - 12 x - 2 \cdot 3 (x^{2} x) - 16 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.7.1.2

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

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Step 1.1.7.1.2.1

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

$6 x^{3} + 24 x^{2} - 12 x - 2 \cdot 3 (x^{2} x^{1}) - 16 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.7.1.2.2

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

$6 x^{3} + 24 x^{2} - 12 x - 2 \cdot 3 x^{2 + 1} - 16 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.7.1.3

Add $2$ and $1$ .

$6 x^{3} + 24 x^{2} - 12 x - 2 \cdot 3 x^{3} - 16 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.1.7.2

Multiply $- 2$ by $3$ .

$6 x^{3} + 24 x^{2} - 12 x - 6 x^{3} - 16 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $6 x^{3} + 24 x^{2} - 12 x - 6 x^{3} - 16 x$ .

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Step 1.2.1.1

Subtract $6 x^{3}$ from $6 x^{3}$ .

$24 x^{2} - 12 x + 0 - 16 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.2.1.2

Add $24 x^{2} - 12 x$ and $0$ .

$24 x^{2} - 12 x - 16 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 1.2.2

Subtract $16 x$ from $- 12 x$ .

$24 x^{2} - 28 x = 8 x (3 x - 4) - 4 (3 x - 8)$

Step 2

Simplify $8 x (3 x - 4) - 4 (3 x - 8)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$24 x^{2} - 28 x = 8 x (3 x) + 8 x \cdot - 4 - 4 (3 x - 8)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$24 x^{2} - 28 x = 8 \cdot 3 x \cdot x + 8 x \cdot - 4 - 4 (3 x - 8)$

Step 2.1.3

Multiply $- 4$ by $8$ .

$24 x^{2} - 28 x = 8 \cdot 3 x \cdot x - 32 x - 4 (3 x - 8)$

Step 2.1.4

Simplify each term.

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Step 2.1.4.1

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

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Step 2.1.4.1.1

Move $x$ .

$24 x^{2} - 28 x = 8 \cdot 3 (x \cdot x) - 32 x - 4 (3 x - 8)$

Step 2.1.4.1.2

Multiply $x$ by $x$ .

$24 x^{2} - 28 x = 8 \cdot 3 x^{2} - 32 x - 4 (3 x - 8)$

Step 2.1.4.2

Multiply $8$ by $3$ .

$24 x^{2} - 28 x = 24 x^{2} - 32 x - 4 (3 x - 8)$

Step 2.1.5

Apply the distributive property.

$24 x^{2} - 28 x = 24 x^{2} - 32 x - 4 (3 x) - 4 \cdot - 8$

Step 2.1.6

Multiply $3$ by $- 4$ .

$24 x^{2} - 28 x = 24 x^{2} - 32 x - 12 x - 4 \cdot - 8$

Step 2.1.7

Multiply $- 4$ by $- 8$ .

$24 x^{2} - 28 x = 24 x^{2} - 32 x - 12 x + 32$

Step 2.2

Subtract $12 x$ from $- 32 x$ .

$24 x^{2} - 28 x = 24 x^{2} - 44 x + 32$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $24 x^{2}$ from both sides of the equation.

$24 x^{2} - 28 x - 24 x^{2} = - 44 x + 32$

Step 3.2

Add $44 x$ to both sides of the equation.

$24 x^{2} - 28 x - 24 x^{2} + 44 x = 32$

Step 3.3

Combine the opposite terms in $24 x^{2} - 28 x - 24 x^{2} + 44 x$ .

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Step 3.3.1

Subtract $24 x^{2}$ from $24 x^{2}$ .

$- 28 x + 0 + 44 x = 32$

Step 3.3.2

Add $- 28 x$ and $0$ .

$- 28 x + 44 x = 32$

Step 3.4

Add $- 28 x$ and $44 x$ .

$16 x = 32$

Step 4

Divide each term in $16 x = 32$ by $16$ and simplify.

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Step 4.1

Divide each term in $16 x = 32$ by $16$ .

$\frac{16 x}{16} = \frac{32}{16}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $16$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{16 x}{16} = \frac{32}{16}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{32}{16}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $32$ by $16$ .

$x = 2$