Simplify 5x(3x^2+6)

$5 x (3 x^{2} + 6)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$5 x (3 x^{2}) + 5 x \cdot 6$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$5 \cdot 3 x \cdot x^{2} + 5 x \cdot 6$

Multiply $6$ by $5$ .

$5 \cdot 3 x \cdot x^{2} + 30 x$

Step 2

Simplify each term.

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

Move $x^{2}$ .

$5 \cdot 3 (x^{2} x) + 30 x$

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

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

$5 \cdot 3 (x^{2} x^{1}) + 30 x$

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

$5 \cdot 3 x^{2 + 1} + 30 x$

Add $2$ and $1$ .

$5 \cdot 3 x^{3} + 30 x$

Multiply $5$ by $3$ .

$15 x^{3} + 30 x$