Simplify 8p(-3p^2+6p-2)

$8 p (- 3 p^{2} + 6 p - 2)$

Step 1

Apply the distributive property.

$8 p (- 3 p^{2}) + 8 p (6 p) + 8 p \cdot - 2$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$8 \cdot - 3 p \cdot p^{2} + 8 p (6 p) + 8 p \cdot - 2$

Rewrite using the commutative property of multiplication.

$8 \cdot - 3 p \cdot p^{2} + 8 \cdot 6 p \cdot p + 8 p \cdot - 2$

Multiply $- 2$ by $8$ .

$8 \cdot - 3 p \cdot p^{2} + 8 \cdot 6 p \cdot p - 16 p$

Step 3

Simplify each term.

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

Move $p^{2}$ .

$8 \cdot - 3 (p^{2} p) + 8 \cdot 6 p \cdot p - 16 p$

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

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

$8 \cdot - 3 (p^{2} p^{1}) + 8 \cdot 6 p \cdot p - 16 p$

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

$8 \cdot - 3 p^{2 + 1} + 8 \cdot 6 p \cdot p - 16 p$

Add $2$ and $1$ .

$8 \cdot - 3 p^{3} + 8 \cdot 6 p \cdot p - 16 p$

Multiply $8$ by $- 3$ .

$- 24 p^{3} + 8 \cdot 6 p \cdot p - 16 p$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$- 24 p^{3} + 8 \cdot 6 (p \cdot p) - 16 p$

Multiply $p$ by $p$ .

$- 24 p^{3} + 8 \cdot 6 p^{2} - 16 p$

Multiply $8$ by $6$ .

$- 24 p^{3} + 48 p^{2} - 16 p$