Algebra Examples

$x (8 x^{2} - 6 x + 3) - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1

Simplify $x (8 x^{2} - 6 x + 3) - 2 x (4 x^{2} - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$x (8 x^{2}) + x (- 6 x) + x \cdot 3 - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.2

Simplify.

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Step 1.1.2.1

Rewrite using the commutative property of multiplication.

$8 x \cdot x^{2} + x (- 6 x) + x \cdot 3 - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.2.2

Rewrite using the commutative property of multiplication.

$8 x \cdot x^{2} - 6 x \cdot x + x \cdot 3 - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.2.3

Move $3$ to the left of $x$ .

$8 x \cdot x^{2} - 6 x \cdot x + 3 \cdot x - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.3

Simplify each term.

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Step 1.1.3.1

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

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Step 1.1.3.1.1

Move $x^{2}$ .

$8 (x^{2} x) - 6 x \cdot x + 3 \cdot x - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.3.1.2

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

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Step 1.1.3.1.2.1

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

$8 (x^{2} x^{1}) - 6 x \cdot x + 3 \cdot x - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.3.1.2.2

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

$8 x^{2 + 1} - 6 x \cdot x + 3 \cdot x - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.3.1.3

Add $2$ and $1$ .

$8 x^{3} - 6 x \cdot x + 3 \cdot x - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.3.2

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

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Step 1.1.3.2.1

Move $x$ .

$8 x^{3} - 6 (x \cdot x) + 3 \cdot x - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.3.2.2

Multiply $x$ by $x$ .

$8 x^{3} - 6 x^{2} + 3 \cdot x - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

$8 x^{3} - 6 x^{2} + 3 x - 2 x (4 x^{2} - 1) = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.4

Apply the distributive property.

$8 x^{3} - 6 x^{2} + 3 x - 2 x (4 x^{2}) - 2 x \cdot - 1 = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.5

Rewrite using the commutative property of multiplication.

$8 x^{3} - 6 x^{2} + 3 x - 2 \cdot 4 x \cdot x^{2} - 2 x \cdot - 1 = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.6

Multiply $- 1$ by $- 2$ .

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

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 $x^{2}$ .

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

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 $1$ .

$8 x^{3} - 6 x^{2} + 3 x - 2 \cdot 4 (x^{2} x^{1}) + 2 x = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.7.1.2.2

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

$8 x^{3} - 6 x^{2} + 3 x - 2 \cdot 4 x^{2 + 1} + 2 x = - 6 x (x + 5) + 5 (3 x + 4)$

Step 1.1.7.1.3

Add $2$ and $1$ .

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

Step 1.1.7.2

Multiply $- 2$ by $4$ .

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

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $8 x^{3} - 6 x^{2} + 3 x - 8 x^{3} + 2 x$ .

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Step 1.2.1.1

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

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

Step 1.2.1.2

Add $- 6 x^{2} + 3 x$ and $0$ .

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

Step 1.2.2

Add $3 x$ and $2 x$ .

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

Step 2

Simplify $- 6 x (x + 5) + 5 (3 x + 4)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Multiply $5$ by $- 6$ .

$- 6 x^{2} + 5 x = - 6 x^{2} - 30 x + 5 (3 x + 4)$

Step 2.1.4

Apply the distributive property.

$- 6 x^{2} + 5 x = - 6 x^{2} - 30 x + 5 (3 x) + 5 \cdot 4$

Step 2.1.5

Multiply $3$ by $5$ .

$- 6 x^{2} + 5 x = - 6 x^{2} - 30 x + 15 x + 5 \cdot 4$

Step 2.1.6

Multiply $5$ by $4$ .

$- 6 x^{2} + 5 x = - 6 x^{2} - 30 x + 15 x + 20$

Step 2.2

Add $- 30 x$ and $15 x$ .

$- 6 x^{2} + 5 x = - 6 x^{2} - 15 x + 20$

Step 3

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

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Step 3.1

Add $6 x^{2}$ to both sides of the equation.

$- 6 x^{2} + 5 x + 6 x^{2} = - 15 x + 20$

Step 3.2

Add $15 x$ to both sides of the equation.

$- 6 x^{2} + 5 x + 6 x^{2} + 15 x = 20$

Step 3.3

Combine the opposite terms in $- 6 x^{2} + 5 x + 6 x^{2} + 15 x$ .

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Step 3.3.1

Add $- 6 x^{2}$ and $6 x^{2}$ .

$5 x + 0 + 15 x = 20$

Step 3.3.2

Add $5 x$ and $0$ .

$5 x + 15 x = 20$

Step 3.4

Add $5 x$ and $15 x$ .

$20 x = 20$

Step 4

Divide each term in $20 x = 20$ by $20$ and simplify.

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Step 4.1

Divide each term in $20 x = 20$ by $20$ .

$\frac{20 x}{20} = \frac{20}{20}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $20$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{20 x}{20} = \frac{20}{20}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{20}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $20$ by $20$ .

$x = 1$