Find the Product (5d-12)(-7+3d)

$(5 d - 12) (- 7 + 3 d)$

Step 1

Expand $(5 d - 12) (- 7 + 3 d)$ using the FOIL Method.

Apply the distributive property.

$5 d (- 7 + 3 d) - 12 (- 7 + 3 d)$

Apply the distributive property.

$5 d \cdot - 7 + 5 d (3 d) - 12 (- 7 + 3 d)$

Apply the distributive property.

$5 d \cdot - 7 + 5 d (3 d) - 12 \cdot - 7 - 12 (3 d)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 7$ by $5$ .

$- 35 d + 5 d (3 d) - 12 \cdot - 7 - 12 (3 d)$

Rewrite using the commutative property of multiplication.

$- 35 d + 5 \cdot 3 d \cdot d - 12 \cdot - 7 - 12 (3 d)$

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

Move $d$ .

$- 35 d + 5 \cdot 3 (d \cdot d) - 12 \cdot - 7 - 12 (3 d)$

Multiply $d$ by $d$ .

$- 35 d + 5 \cdot 3 d^{2} - 12 \cdot - 7 - 12 (3 d)$

Multiply $5$ by $3$ .

$- 35 d + 15 d^{2} - 12 \cdot - 7 - 12 (3 d)$

Multiply $- 12$ by $- 7$ .

$- 35 d + 15 d^{2} + 84 - 12 (3 d)$

Multiply $3$ by $- 12$ .

$- 35 d + 15 d^{2} + 84 - 36 d$

Subtract $36 d$ from $- 35 d$ .

$- 71 d + 15 d^{2} + 84$