Find the Product (3d+2)(d^2-1)

$(3 d + 2) (d^{2} - 1)$

Step 1

Expand $(3 d + 2) (d^{2} - 1)$ using the FOIL Method.

Apply the distributive property.

$3 d (d^{2} - 1) + 2 (d^{2} - 1)$

Apply the distributive property.

$3 d \cdot d^{2} + 3 d \cdot - 1 + 2 (d^{2} - 1)$

Apply the distributive property.

$3 d \cdot d^{2} + 3 d \cdot - 1 + 2 d^{2} + 2 \cdot - 1$

Step 2

Simplify each term.

Multiply $d$ by $d^{2}$ by adding the exponents.

Move $d^{2}$ .

$3 (d^{2} d) + 3 d \cdot - 1 + 2 d^{2} + 2 \cdot - 1$

Multiply $d^{2}$ by $d$ .

Raise $d$ to the power of $1$ .

$3 (d^{2} d^{1}) + 3 d \cdot - 1 + 2 d^{2} + 2 \cdot - 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 d^{2 + 1} + 3 d \cdot - 1 + 2 d^{2} + 2 \cdot - 1$

Add $2$ and $1$ .

$3 d^{3} + 3 d \cdot - 1 + 2 d^{2} + 2 \cdot - 1$

Multiply $- 1$ by $3$ .

$3 d^{3} - 3 d + 2 d^{2} + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$3 d^{3} - 3 d + 2 d^{2} - 2$