Simplify -3x(-8x^2+5x+3)

$- 3 x (- 8 x^{2} + 5 x + 3)$

Step 1

Apply the distributive property.

$- 3 x (- 8 x^{2}) - 3 x (5 x) - 3 x \cdot 3$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 8 x \cdot x^{2} - 3 x (5 x) - 3 x \cdot 3$

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 8 x \cdot x^{2} - 3 \cdot 5 x \cdot x - 3 x \cdot 3$

Multiply $3$ by $- 3$ .

$- 3 \cdot - 8 x \cdot x^{2} - 3 \cdot 5 x \cdot x - 9 x$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$- 3 \cdot - 8 (x^{2} x) - 3 \cdot 5 x \cdot x - 9 x$

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

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

$- 3 \cdot - 8 (x^{2} x^{1}) - 3 \cdot 5 x \cdot x - 9 x$

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

$- 3 \cdot - 8 x^{2 + 1} - 3 \cdot 5 x \cdot x - 9 x$

Add $2$ and $1$ .

$- 3 \cdot - 8 x^{3} - 3 \cdot 5 x \cdot x - 9 x$

Multiply $- 3$ by $- 8$ .

$24 x^{3} - 3 \cdot 5 x \cdot x - 9 x$

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

Move $x$ .

$24 x^{3} - 3 \cdot 5 (x \cdot x) - 9 x$

Multiply $x$ by $x$ .

$24 x^{3} - 3 \cdot 5 x^{2} - 9 x$

Multiply $- 3$ by $5$ .

$24 x^{3} - 15 x^{2} - 9 x$