Simplify -8mn*(2m-3mp+p^2)

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

Step 1

Apply the distributive property.

$- 8 m n (2 m) - 8 m n (- 3 m p) - 8 m n p^{2}$

Step 2

Simplify.

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$- 8 (m \cdot m) n \cdot 2 - 8 m n (- 3 m p) - 8 m n p^{2}$

Multiply $m$ by $m$ .

$- 8 m^{2} n \cdot 2 - 8 m n (- 3 m p) - 8 m n p^{2}$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$- 8 m^{2} n \cdot 2 - 8 (m \cdot m) n (- 3 p) - 8 m n p^{2}$

Multiply $m$ by $m$ .

$- 8 m^{2} n \cdot 2 - 8 m^{2} n (- 3 p) - 8 m n p^{2}$

Step 3

Simplify each term.

Multiply $2$ by $- 8$ .

$- 16 m^{2} n - 8 m^{2} n (- 3 p) - 8 m n p^{2}$

Multiply $- 3$ by $- 8$ .

$- 16 m^{2} n + 24 m^{2} n p - 8 m n p^{2}$