Simplify (3d+3)(2d^2+5d-2)

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $d^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $3$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $d$ .

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

Multiply $d$ by $d$ .

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

Multiply $3$ by $5$ .

$6 d^{3} + 15 d^{2} + 3 d \cdot - 2 + 3 (2 d^{2}) + 3 (5 d) + 3 \cdot - 2$

Multiply $- 2$ by $3$ .

$6 d^{3} + 15 d^{2} - 6 d + 3 (2 d^{2}) + 3 (5 d) + 3 \cdot - 2$

Multiply $2$ by $3$ .

$6 d^{3} + 15 d^{2} - 6 d + 6 d^{2} + 3 (5 d) + 3 \cdot - 2$

Multiply $5$ by $3$ .

$6 d^{3} + 15 d^{2} - 6 d + 6 d^{2} + 15 d + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$6 d^{3} + 15 d^{2} - 6 d + 6 d^{2} + 15 d - 6$

Simplify by adding terms.

Add $15 d^{2}$ and $6 d^{2}$ .

$6 d^{3} + 21 d^{2} - 6 d + 15 d - 6$

Add $- 6 d$ and $15 d$ .

$6 d^{3} + 21 d^{2} + 9 d - 6$