Simplify 2x^3(5x-1)

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $2$ .

$2 \cdot 5 x^{3} x - 2 x^{3}$

Step 2

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $3$ .

$2 \cdot 5 x^{4} - 2 x^{3}$

Multiply $2$ by $5$ .

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