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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $5$ by $- 4$ .

$- 4 \cdot 2 x \cdot x^{2} - 4 \cdot - 3 x \cdot x - 20 x$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$- 4 \cdot 2 (x^{2} x) - 4 \cdot - 3 x \cdot x - 20 x$

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

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

$- 4 \cdot 2 (x^{2} x^{1}) - 4 \cdot - 3 x \cdot x - 20 x$

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

$- 4 \cdot 2 x^{2 + 1} - 4 \cdot - 3 x \cdot x - 20 x$

Add $2$ and $1$ .

$- 4 \cdot 2 x^{3} - 4 \cdot - 3 x \cdot x - 20 x$

Multiply $- 4$ by $2$ .

$- 8 x^{3} - 4 \cdot - 3 x \cdot x - 20 x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 8 x^{3} - 4 \cdot - 3 (x \cdot x) - 20 x$

Multiply $x$ by $x$ .

$- 8 x^{3} - 4 \cdot - 3 x^{2} - 20 x$

Multiply $- 4$ by $- 3$ .

$- 8 x^{3} + 12 x^{2} - 20 x$