Find the Product 4d(d^3-d^2)

$4 d (d^{3} - d^{2})$

Step 1

Apply the distributive property.

$4 d \cdot d^{3} + 4 d (- d^{2})$

Step 2

Multiply $d$ by $d^{3}$ by adding the exponents.

Move $d^{3}$ .

$4 (d^{3} d) + 4 d (- d^{2})$

Multiply $d^{3}$ by $d$ .

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

$4 (d^{3} d^{1}) + 4 d (- d^{2})$

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

$4 d^{3 + 1} + 4 d (- d^{2})$

Add $3$ and $1$ .

$4 d^{4} + 4 d (- d^{2})$

Step 3

Rewrite using the commutative property of multiplication.

$4 d^{4} + 4 \cdot - 1 d \cdot d^{2}$

Step 4

Simplify each term.

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

Move $d^{2}$ .

$4 d^{4} + 4 \cdot - 1 (d^{2} d)$

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

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

$4 d^{4} + 4 \cdot - 1 (d^{2} d^{1})$

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

$4 d^{4} + 4 \cdot - 1 d^{2 + 1}$

Add $2$ and $1$ .

$4 d^{4} + 4 \cdot - 1 d^{3}$

Multiply $4$ by $- 1$ .

$4 d^{4} - 4 d^{3}$