Expand the Trigonometric Expression (-6d+6)(2d-2)

$(- 6 d + 6) (2 d - 2)$

Step 1

Expand $(- 6 d + 6) (2 d - 2)$ using the FOIL Method.

Apply the distributive property.

$- 6 d (2 d - 2) + 6 (2 d - 2)$

Apply the distributive property.

$- 6 d (2 d) - 6 d \cdot - 2 + 6 (2 d - 2)$

Apply the distributive property.

$- 6 d (2 d) - 6 d \cdot - 2 + 6 (2 d) + 6 \cdot - 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 6 \cdot 2 d \cdot d - 6 d \cdot - 2 + 6 (2 d) + 6 \cdot - 2$

Multiply $d$ by $d$ by adding the exponents.

Move $d$ .

$- 6 \cdot 2 (d \cdot d) - 6 d \cdot - 2 + 6 (2 d) + 6 \cdot - 2$

Multiply $d$ by $d$ .

$- 6 \cdot 2 d^{2} - 6 d \cdot - 2 + 6 (2 d) + 6 \cdot - 2$

Multiply $- 6$ by $2$ .

$- 12 d^{2} - 6 d \cdot - 2 + 6 (2 d) + 6 \cdot - 2$

Multiply $- 2$ by $- 6$ .

$- 12 d^{2} + 12 d + 6 (2 d) + 6 \cdot - 2$

Multiply $2$ by $6$ .

$- 12 d^{2} + 12 d + 12 d + 6 \cdot - 2$

Multiply $6$ by $- 2$ .

$- 12 d^{2} + 12 d + 12 d - 12$

Add $12 d$ and $12 d$ .

$- 12 d^{2} + 24 d - 12$