Find the Product (6-d)(d^2-5+3d)

$(6 - d) (d^{2} - 5 + 3 d)$

Step 1

Expand $(6 - d) (d^{2} - 5 + 3 d)$ by multiplying each term in the first expression by each term in the second expression.

$6 d^{2} + 6 \cdot - 5 + 6 (3 d) - d \cdot d^{2} - d \cdot - 5 - d (3 d)$

Step 2

Simplify terms.

Simplify each term.

Multiply $6$ by $- 5$ .

$6 d^{2} - 30 + 6 (3 d) - d \cdot d^{2} - d \cdot - 5 - d (3 d)$

Multiply $3$ by $6$ .

$6 d^{2} - 30 + 18 d - d \cdot d^{2} - d \cdot - 5 - d (3 d)$

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

Move $d^{2}$ .

$6 d^{2} - 30 + 18 d - (d^{2} d) - d \cdot - 5 - d (3 d)$

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

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

$6 d^{2} - 30 + 18 d - (d^{2} d^{1}) - d \cdot - 5 - d (3 d)$

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

$6 d^{2} - 30 + 18 d - d^{2 + 1} - d \cdot - 5 - d (3 d)$

Add $2$ and $1$ .

$6 d^{2} - 30 + 18 d - d^{3} - d \cdot - 5 - d (3 d)$

Multiply $- 5$ by $- 1$ .

$6 d^{2} - 30 + 18 d - d^{3} + 5 d - d (3 d)$

Rewrite using the commutative property of multiplication.

$6 d^{2} - 30 + 18 d - d^{3} + 5 d - 1 \cdot 3 d \cdot d$

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

Move $d$ .

$6 d^{2} - 30 + 18 d - d^{3} + 5 d - 1 \cdot 3 (d \cdot d)$

Multiply $d$ by $d$ .

$6 d^{2} - 30 + 18 d - d^{3} + 5 d - 1 \cdot 3 d^{2}$

Multiply $- 1$ by $3$ .

$6 d^{2} - 30 + 18 d - d^{3} + 5 d - 3 d^{2}$

Simplify by adding terms.

Subtract $3 d^{2}$ from $6 d^{2}$ .

$3 d^{2} - 30 + 18 d - d^{3} + 5 d$

Add $18 d$ and $5 d$ .

$3 d^{2} - 30 - d^{3} + 23 d$