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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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

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

Add $2$ and $3$ .

$x^{5} + x^{2} (2 x) - 1 x^{3} - 1 (2 x)$

Rewrite using the commutative property of multiplication.

$x^{5} + 2 x^{2} x - 1 x^{3} - 1 (2 x)$

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

Move $x$ .

$x^{5} + 2 (x \cdot x^{2}) - 1 x^{3} - 1 (2 x)$

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

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

$x^{5} + 2 (x^{1} x^{2}) - 1 x^{3} - 1 (2 x)$

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

$x^{5} + 2 x^{1 + 2} - 1 x^{3} - 1 (2 x)$

Add $1$ and $2$ .

$x^{5} + 2 x^{3} - 1 x^{3} - 1 (2 x)$

Rewrite $- 1 x^{3}$ as $- x^{3}$ .

$x^{5} + 2 x^{3} - x^{3} - 1 (2 x)$

Multiply $2$ by $- 1$ .

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

Subtract $x^{3}$ from $2 x^{3}$ .

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