Simplify (3q+2)(9q^2-12q+4)

$(3 q + 2) (9 q^{2} - 12 q + 4)$

Step 1

Expand $(3 q + 2) (9 q^{2} - 12 q + 4)$ by multiplying each term in the first expression by each term in the second expression.

$3 q (9 q^{2}) + 3 q (- 12 q) + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 9 q \cdot q^{2} + 3 q (- 12 q) + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

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

Move $q^{2}$ .

$3 \cdot 9 (q^{2} q) + 3 q (- 12 q) + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

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

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

$3 \cdot 9 (q^{2} q^{1}) + 3 q (- 12 q) + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

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

$3 \cdot 9 q^{2 + 1} + 3 q (- 12 q) + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Add $2$ and $1$ .

$3 \cdot 9 q^{3} + 3 q (- 12 q) + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Multiply $3$ by $9$ .

$27 q^{3} + 3 q (- 12 q) + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Rewrite using the commutative property of multiplication.

$27 q^{3} + 3 \cdot - 12 q \cdot q + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Multiply $q$ by $q$ by adding the exponents.

Move $q$ .

$27 q^{3} + 3 \cdot - 12 (q \cdot q) + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Multiply $q$ by $q$ .

$27 q^{3} + 3 \cdot - 12 q^{2} + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Multiply $3$ by $- 12$ .

$27 q^{3} - 36 q^{2} + 3 q \cdot 4 + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Multiply $4$ by $3$ .

$27 q^{3} - 36 q^{2} + 12 q + 2 (9 q^{2}) + 2 (- 12 q) + 2 \cdot 4$

Multiply $9$ by $2$ .

$27 q^{3} - 36 q^{2} + 12 q + 18 q^{2} + 2 (- 12 q) + 2 \cdot 4$

Multiply $- 12$ by $2$ .

$27 q^{3} - 36 q^{2} + 12 q + 18 q^{2} - 24 q + 2 \cdot 4$

Multiply $2$ by $4$ .

$27 q^{3} - 36 q^{2} + 12 q + 18 q^{2} - 24 q + 8$

Simplify by adding terms.

Add $- 36 q^{2}$ and $18 q^{2}$ .

$27 q^{3} - 18 q^{2} + 12 q - 24 q + 8$

Subtract $24 q$ from $12 q$ .

$27 q^{3} - 18 q^{2} - 12 q + 8$