Expand the Trigonometric Expression (-5d+8)(d-3)

$(- 5 d + 8) (d - 3)$

Step 1

Expand $(- 5 d + 8) (d - 3)$ using the FOIL Method.

Apply the distributive property.

$- 5 d (d - 3) + 8 (d - 3)$

Apply the distributive property.

$- 5 d \cdot d - 5 d \cdot - 3 + 8 (d - 3)$

Apply the distributive property.

$- 5 d \cdot d - 5 d \cdot - 3 + 8 d + 8 \cdot - 3$

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $d$ .

$- 5 (d \cdot d) - 5 d \cdot - 3 + 8 d + 8 \cdot - 3$

Multiply $d$ by $d$ .

$- 5 d^{2} - 5 d \cdot - 3 + 8 d + 8 \cdot - 3$

Multiply $- 3$ by $- 5$ .

$- 5 d^{2} + 15 d + 8 d + 8 \cdot - 3$

Multiply $8$ by $- 3$ .

$- 5 d^{2} + 15 d + 8 d - 24$

Add $15 d$ and $8 d$ .

$- 5 d^{2} + 23 d - 24$