Simplify -2x(x+1)+4x^2(x+3)-x^2-(x-3)

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

Step 1

Simplify each term.

Apply the distributive property.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $1$ .

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

Apply the distributive property.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $3$ by $4$ .

$- 2 x^{2} - 2 x + 4 x^{3} + 12 x^{2} - x^{2} - (x - 3)$

Apply the distributive property.

$- 2 x^{2} - 2 x + 4 x^{3} + 12 x^{2} - x^{2} - x - - 3$

Multiply $- 1$ by $- 3$ .

$- 2 x^{2} - 2 x + 4 x^{3} + 12 x^{2} - x^{2} - x + 3$

Step 2

Simplify by adding terms.

Add $- 2 x^{2}$ and $12 x^{2}$ .

$10 x^{2} - 2 x + 4 x^{3} - x^{2} - x + 3$

Subtract $x^{2}$ from $10 x^{2}$ .

$9 x^{2} - 2 x + 4 x^{3} - x + 3$

Subtract $x$ from $- 2 x$ .

$9 x^{2} + 4 x^{3} - 3 x + 3$

Reorder $9 x^{2}$ and $4 x^{3}$ .

$4 x^{3} + 9 x^{2} - 3 x + 3$