Algebra Examples

w^{3} - w (w^{2} + 2 w - 1) + 2 w

$w^{3} - w (w^{2} + 2 w - 1) + 2 w$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply

w

$w$ by

w^{2}

$w^{2}$ by adding the exponents.

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Step 1.2.1.1

Move

w^{2}

$w^{2}$ .

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

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

Step 1.2.1.2

Multiply

w^{2}

$w^{2}$ by

w

$w$ .

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Step 1.2.1.2.1

Raise

w

$w$ to the power of

1

$1$ .

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

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

Step 1.2.1.2.2

Use the power rule

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

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

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

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

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

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

Step 1.2.1.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

Step 1.2.2

Rewrite using the commutative property of multiplication.

w^{3} - w^{3} - 1 \cdot 2 w \cdot w - w \cdot - 1 + 2 w

$w^{3} - w^{3} - 1 \cdot 2 w \cdot w - w \cdot - 1 + 2 w$

Step 1.2.3

Multiply

- w \cdot - 1

$- w \cdot - 1$ .

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Step 1.2.3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

w^{3} - w^{3} - 1 \cdot 2 w \cdot w + 1 w + 2 w

$w^{3} - w^{3} - 1 \cdot 2 w \cdot w + 1 w + 2 w$

Step 1.2.3.2

Multiply

w

$w$ by

1

$1$ .

w^{3} - w^{3} - 1 \cdot 2 w \cdot w + w + 2 w

$w^{3} - w^{3} - 1 \cdot 2 w \cdot w + w + 2 w$

w^{3} - w^{3} - 1 \cdot 2 w \cdot w + w + 2 w

$w^{3} - w^{3} - 1 \cdot 2 w \cdot w + w + 2 w$

w^{3} - w^{3} - 1 \cdot 2 w \cdot w + w + 2 w

$w^{3} - w^{3} - 1 \cdot 2 w \cdot w + w + 2 w$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply

w

$w$ by

w

$w$ by adding the exponents.

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Step 1.3.1.1

Move

w

$w$ .

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

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

Step 1.3.1.2

Multiply

w

$w$ by

w

$w$ .

w^{3} - w^{3} - 1 \cdot 2 w^{2} + w + 2 w

$w^{3} - w^{3} - 1 \cdot 2 w^{2} + w + 2 w$

w^{3} - w^{3} - 1 \cdot 2 w^{2} + w + 2 w

$w^{3} - w^{3} - 1 \cdot 2 w^{2} + w + 2 w$

Step 1.3.2

Multiply

- 1

$- 1$ by

2

$2$ .

w^{3} - w^{3} - 2 w^{2} + w + 2 w

$w^{3} - w^{3} - 2 w^{2} + w + 2 w$

w^{3} - w^{3} - 2 w^{2} + w + 2 w

$w^{3} - w^{3} - 2 w^{2} + w + 2 w$

w^{3} - w^{3} - 2 w^{2} + w + 2 w

$w^{3} - w^{3} - 2 w^{2} + w + 2 w$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract

w^{3}

$w^{3}$ from

w^{3}

$w^{3}$ .

0 - 2 w^{2} + w + 2 w

$0 - 2 w^{2} + w + 2 w$

Step 2.2

Subtract

2 w^{2}

$2 w^{2}$ from

0

$0$ .

- 2 w^{2} + w + 2 w

$- 2 w^{2} + w + 2 w$

Step 2.3

Add

w

$w$ and

2 w

$2 w$ .

- 2 w^{2} + 3 w

$- 2 w^{2} + 3 w$

- 2 w^{2} + 3 w

$- 2 w^{2} + 3 w$