Simplify 1/4*(n(-24+8m-100p))

$\frac{1}{4} \cdot (n (- 24 + 8 m - 100 p))$

Step 1

Apply the distributive property.

$\frac{1}{4} \cdot (n \cdot - 24 + n (8 m) + n (- 100 p))$

Step 2

Simplify.

Move $- 24$ to the left of $n$ .

$\frac{1}{4} \cdot (- 24 \cdot n + n (8 m) + n (- 100 p))$

Rewrite using the commutative property of multiplication.

$\frac{1}{4} \cdot (- 24 \cdot n + 8 n m + n (- 100 p))$

Rewrite using the commutative property of multiplication.

$\frac{1}{4} \cdot (- 24 \cdot n + 8 n m - 100 n p)$

Step 3

Apply the distributive property.

$\frac{1}{4} (- 24 n) + \frac{1}{4} (8 n m) + \frac{1}{4} (- 100 n p)$

Step 4

Simplify.

Cancel the common factor of $4$ .

Factor $4$ out of $- 24 n$ .

$\frac{1}{4} (4 (- 6 n)) + \frac{1}{4} (8 n m) + \frac{1}{4} (- 100 n p)$

Cancel the common factor.

$\frac{1}{4} (4 (- 6 n)) + \frac{1}{4} (8 n m) + \frac{1}{4} (- 100 n p)$

Rewrite the expression.

$- 6 n + \frac{1}{4} (8 n m) + \frac{1}{4} (- 100 n p)$

Cancel the common factor of $4$ .

Factor $4$ out of $8 n m$ .

$- 6 n + \frac{1}{4} (4 (2 n m)) + \frac{1}{4} (- 100 n p)$

Cancel the common factor.

$- 6 n + \frac{1}{4} (4 (2 n m)) + \frac{1}{4} (- 100 n p)$

Rewrite the expression.

$- 6 n + 2 n m + \frac{1}{4} (- 100 n p)$

Cancel the common factor of $4$ .

Factor $4$ out of $- 100 n p$ .

$- 6 n + 2 n m + \frac{1}{4} (4 (- 25 n p))$

Cancel the common factor.

$- 6 n + 2 n m + \frac{1}{4} (4 (- 25 n p))$

Rewrite the expression.

$- 6 n + 2 n m - 25 n p$

Step 5

Move $n$ .

$- 6 n + 2 m n - 25 n p$

Step 6

Move $- 6 n$ .

$2 m n - 25 n p - 6 n$