Algebra Examples

$3 x (2 x^{2} - 4 x + 2) - (5 x^{2} - 7 x - 8)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 x (2 x^{2}) + 3 x (- 4 x) + 3 x \cdot 2 - (5 x^{2} - 7 x - 8)$

Step 1.2

Simplify.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x^{2} + 3 x (- 4 x) + 3 x \cdot 2 - (5 x^{2} - 7 x - 8)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x^{2} + 3 \cdot - 4 x \cdot x + 3 x \cdot 2 - (5 x^{2} - 7 x - 8)$

Step 1.2.3

Multiply $2$ by $3$ .

$3 \cdot 2 x \cdot x^{2} + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $x^{2}$ .

$3 \cdot 2 (x^{2} x) + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.3.1.2

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

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Step 1.3.1.2.1

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

$3 \cdot 2 (x^{2} x^{1}) + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.3.1.2.2

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

$3 \cdot 2 x^{2 + 1} + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.3.1.3

Add $2$ and $1$ .

$3 \cdot 2 x^{3} + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.3.2

Multiply $3$ by $2$ .

$6 x^{3} + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.3.3

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

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Step 1.3.3.1

Move $x$ .

$6 x^{3} + 3 \cdot - 4 (x \cdot x) + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.3.3.2

Multiply $x$ by $x$ .

$6 x^{3} + 3 \cdot - 4 x^{2} + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.3.4

Multiply $3$ by $- 4$ .

$6 x^{3} - 12 x^{2} + 6 x - (5 x^{2} - 7 x - 8)$

Step 1.4

Apply the distributive property.

$6 x^{3} - 12 x^{2} + 6 x - (5 x^{2}) - (- 7 x) - - 8$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $5$ by $- 1$ .

$6 x^{3} - 12 x^{2} + 6 x - 5 x^{2} - (- 7 x) - - 8$

Step 1.5.2

Multiply $- 7$ by $- 1$ .

$6 x^{3} - 12 x^{2} + 6 x - 5 x^{2} + 7 x - - 8$

Step 1.5.3

Multiply $- 1$ by $- 8$ .

$6 x^{3} - 12 x^{2} + 6 x - 5 x^{2} + 7 x + 8$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 x^{2}$ from $- 12 x^{2}$ .

$6 x^{3} - 17 x^{2} + 6 x + 7 x + 8$

Step 2.2

Add $6 x$ and $7 x$ .

$6 x^{3} - 17 x^{2} + 13 x + 8$