Simplify w^3-w(w^2+2w-1)+2w

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

Step 1

Simplify each term.

Apply the distributive property.

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

Simplify.

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

Move $w^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- w \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $w$ by $1$ .

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

Simplify each term.

Multiply $w$ by $w$ by adding the exponents.

Move $w$ .

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

Multiply $w$ by $w$ .

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

Multiply $- 1$ by $2$ .

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

Step 2

Simplify by adding terms.

Subtract $w^{3}$ from $w^{3}$ .

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

Subtract $2 w^{2}$ from $0$ .

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

Add $w$ and $2 w$ .

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