Expand the Trigonometric Expression 3/2a(8b-2c-14d)

$\frac{3}{2} a (8 b - 2 c - 14 d)$

Step 1

Combine $\frac{3}{2}$ and $a$ .

$\frac{3 a}{2} (8 b - 2 c - 14 d)$

Step 2

Apply the distributive property.

$\frac{3 a}{2} (8 b) + \frac{3 a}{2} (- 2 c) + \frac{3 a}{2} (- 14 d)$

Step 3

Simplify.

Rewrite using the commutative property of multiplication.

$8 \frac{3 a}{2} b + \frac{3 a}{2} (- 2 c) + \frac{3 a}{2} (- 14 d)$

Rewrite using the commutative property of multiplication.

$8 \frac{3 a}{2} b - 2 \frac{3 a}{2} c + \frac{3 a}{2} (- 14 d)$

Rewrite using the commutative property of multiplication.

$8 \frac{3 a}{2} b - 2 \frac{3 a}{2} c - 14 \frac{3 a}{2} d$

Step 4

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$2 (4) \frac{3 a}{2} b - 2 \frac{3 a}{2} c - 14 \frac{3 a}{2} d$

Cancel the common factor.

$2 \cdot 4 \frac{3 a}{2} b - 2 \frac{3 a}{2} c - 14 \frac{3 a}{2} d$

Rewrite the expression.

$4 (3 a) b - 2 \frac{3 a}{2} c - 14 \frac{3 a}{2} d$

Multiply $3$ by $4$ .

$12 a b - 2 \frac{3 a}{2} c - 14 \frac{3 a}{2} d$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$12 a b + 2 (- 1) \frac{3 a}{2} c - 14 \frac{3 a}{2} d$

Cancel the common factor.

$12 a b + 2 \cdot - 1 \frac{3 a}{2} c - 14 \frac{3 a}{2} d$

Rewrite the expression.

$12 a b - (3 a) c - 14 \frac{3 a}{2} d$

Multiply $3$ by $- 1$ .

$12 a b - 3 a c - 14 \frac{3 a}{2} d$

Cancel the common factor of $2$ .

Factor $2$ out of $- 14$ .

$12 a b - 3 a c + 2 (- 7) \frac{3 a}{2} d$

Cancel the common factor.

$12 a b - 3 a c + 2 \cdot - 7 \frac{3 a}{2} d$

Rewrite the expression.

$12 a b - 3 a c - 7 (3 a) d$

Multiply $3$ by $- 7$ .

$12 a b - 3 a c - 21 a d$