Find the Product -5x^3(2x^3-4x^2+2)

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

Apply the distributive property.

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

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 5$ .

$- 5 \cdot 2 x^{3} x^{3} - 5 \cdot - 4 x^{3} x^{2} - 10 x^{3}$

Simplify each term.

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

Move $x^{3}$ .

$- 5 \cdot 2 (x^{3} x^{3}) - 5 \cdot - 4 x^{3} x^{2} - 10 x^{3}$

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

$- 5 \cdot 2 x^{3 + 3} - 5 \cdot - 4 x^{3} x^{2} - 10 x^{3}$

Add $3$ and $3$ .

$- 5 \cdot 2 x^{6} - 5 \cdot - 4 x^{3} x^{2} - 10 x^{3}$

Multiply $- 5$ by $2$ .

$- 10 x^{6} - 5 \cdot - 4 x^{3} x^{2} - 10 x^{3}$

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

Move $x^{2}$ .

$- 10 x^{6} - 5 \cdot - 4 (x^{2} x^{3}) - 10 x^{3}$

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

$- 10 x^{6} - 5 \cdot - 4 x^{2 + 3} - 10 x^{3}$

Add $2$ and $3$ .

$- 10 x^{6} - 5 \cdot - 4 x^{5} - 10 x^{3}$

Multiply $- 5$ by $- 4$ .

$- 10 x^{6} + 20 x^{5} - 10 x^{3}$