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

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

Simplify each term.

Expand $(x + 2) (x^{3} - 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

Multiply $x$ by $x^{3}$ by adding the exponents.

Multiply $x$ by $x^{3}$ .

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

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

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

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

Add $1$ and $3$ .

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

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $2$ by $- 1$ .

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

Apply the distributive property.

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

Simplify.

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $- 2$ .

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

Simplify by adding terms.

Add $x$ and $x$ .

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

Simplify the expression.

Add $3$ and $2$ .

$2 x - x^{4} - 2 x^{3} + 5$

Move $2 x$ .

$- x^{4} - 2 x^{3} + 2 x + 5$