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

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

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

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

Move $x$ .

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

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

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

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

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

$2 x^{5} + 3 x^{1 + 3}$

Add $1$ and $3$ .

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