Algebra Examples

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

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

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)

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

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

Step 1.3

Multiply

3

$3$ by

- 1

$- 1$ .

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

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

Step 1.4

Multiply

x^{2}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 1.4.1

Move

x

$x$ .

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

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

Step 1.4.2

Multiply

x

$x$ by

x^{2}

$x^{2}$ .

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Step 1.4.2.1

Raise

x

$x$ to the power of

1

$1$ .

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

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

Step 1.4.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

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

Step 1.4.3

Add

1

$1$ and

2

$2$ .

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

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

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

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

Step 1.5

Apply the distributive property.

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

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

Step 1.6

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

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

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

Step 1.7

Apply the distributive property.

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

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

Step 1.8

Rewrite using the commutative property of multiplication.

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

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

Step 1.9

Multiply

2

$2$ by

2

$2$ .

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

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

Step 1.10

Simplify each term.

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Step 1.10.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 1.10.1.1

Move

x

$x$ .

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

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

Step 1.10.1.2

Multiply

x

$x$ by

x^{2}

$x^{2}$ .

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Step 1.10.1.2.1

Raise

x

$x$ to the power of

1

$1$ .

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

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

Step 1.10.1.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

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

Step 1.10.1.3

Add

1

$1$ and

2

$2$ .

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

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

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

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

Step 1.10.2

Multiply

- 1

$- 1$ by

2

$2$ .

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

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

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

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

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

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract

2 x^{3}

$2 x^{3}$ from

3 x^{3}

$3 x^{3}$ .

x^{3} - 3 x + 4 x

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

Step 2.2

Add

- 3 x

$- 3 x$ and

4 x

$4 x$ .

x^{3} + x

$x^{3} + x$

x^{3} + x

$x^{3} + x$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$