Algebra Examples

$(x^{2} - 1) \cdot 3 x - (x^{2} - 2) \cdot 2 x$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x^{2} (3 x) - 1 (3 x) - (x^{2} - 2) \cdot (2 x)$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 x^{2} x - 1 (3 x) - (x^{2} - 2) \cdot (2 x)$

Step 1.3

Multiply $3$ by $- 1$ .

$3 x^{2} x - 3 x - (x^{2} - 2) \cdot (2 x)$

Step 1.4

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

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Step 1.4.1

Move $x$ .

$3 (x \cdot x^{2}) - 3 x - (x^{2} - 2) \cdot (2 x)$

Step 1.4.2

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

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Step 1.4.2.1

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

$3 (x^{1} x^{2}) - 3 x - (x^{2} - 2) \cdot (2 x)$

Step 1.4.2.2

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

$3 x^{1 + 2} - 3 x - (x^{2} - 2) \cdot (2 x)$

Step 1.4.3

Add $1$ and $2$ .

$3 x^{3} - 3 x - (x^{2} - 2) \cdot (2 x)$

Step 1.5

Apply the distributive property.

$3 x^{3} - 3 x + (- x^{2} - - 2) \cdot (2 x)$

Step 1.6

Multiply $- 1$ by $- 2$ .

$3 x^{3} - 3 x + (- x^{2} + 2) \cdot (2 x)$

Step 1.7

Apply the distributive property.

$3 x^{3} - 3 x - x^{2} (2 x) + 2 (2 x)$

Step 1.8

Rewrite using the commutative property of multiplication.

$3 x^{3} - 3 x - 1 \cdot 2 x^{2} x + 2 (2 x)$

Step 1.9

Multiply $2$ by $2$ .

$3 x^{3} - 3 x - 1 \cdot 2 x^{2} x + 4 x$

Step 1.10

Simplify each term.

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Step 1.10.1

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

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Step 1.10.1.1

Move $x$ .

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

Step 1.10.1.2

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

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Step 1.10.1.2.1

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

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

Step 1.10.1.2.2

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

$3 x^{3} - 3 x - 1 \cdot 2 x^{1 + 2} + 4 x$

Step 1.10.1.3

Add $1$ and $2$ .

$3 x^{3} - 3 x - 1 \cdot 2 x^{3} + 4 x$

Step 1.10.2

Multiply $- 1$ by $2$ .

$3 x^{3} - 3 x - 2 x^{3} + 4 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{3}$ from $3 x^{3}$ .

$x^{3} - 3 x + 4 x$

Step 2.2

Add $- 3 x$ and $4 x$ .

$x^{3} + x$