Simplify -mnp(3m-5n+7p)

$- m n p (3 m - 5 n + 7 p)$

Step 1

Apply the distributive property.

$- m n p (3 m) - m n p (- 5 n) - m n p (7 p)$

Step 2

Simplify.

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

Move $m$ .

$- (m \cdot m) n p \cdot 3 - m n p (- 5 n) - m n p (7 p)$

Multiply $m$ by $m$ .

$- m^{2} n p \cdot 3 - m n p (- 5 n) - m n p (7 p)$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$- m^{2} n p \cdot 3 - m (n \cdot n) p \cdot - 5 - m n p (7 p)$

Multiply $n$ by $n$ .

$- m^{2} n p \cdot 3 - m n^{2} p \cdot - 5 - m n p (7 p)$

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

Move $p$ .

$- m^{2} n p \cdot 3 - m n^{2} p \cdot - 5 - m n (p \cdot p) \cdot 7$

Multiply $p$ by $p$ .

$- m^{2} n p \cdot 3 - m n^{2} p \cdot - 5 - m n p^{2} \cdot 7$

Step 3

Simplify each term.

Multiply $3$ by $- 1$ .

$- 3 m^{2} n p - m n^{2} p \cdot - 5 - m n p^{2} \cdot 7$

Multiply $- 5$ by $- 1$ .

$- 3 m^{2} n p + 5 m n^{2} p - m n p^{2} \cdot 7$

Multiply $7$ by $- 1$ .

$- 3 m^{2} n p + 5 m n^{2} p - 7 m n p^{2}$