Find the Product (x^2+6x+9)(3x-1)

$(x^{2} + 6 x + 9) (3 x - 1)$

Expand $(x^{2} + 6 x + 9) (3 x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} (3 x) + x^{2} \cdot - 1 + 6 x (3 x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 x^{2} x + x^{2} \cdot - 1 + 6 x (3 x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

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

Move $x$ .

$3 (x \cdot x^{2}) + x^{2} \cdot - 1 + 6 x (3 x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

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

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

$3 (x^{1} x^{2}) + x^{2} \cdot - 1 + 6 x (3 x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

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

$3 x^{1 + 2} + x^{2} \cdot - 1 + 6 x (3 x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Add $1$ and $2$ .

$3 x^{3} + x^{2} \cdot - 1 + 6 x (3 x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Move $- 1$ to the left of $x^{2}$ .

$3 x^{3} - 1 \cdot x^{2} + 6 x (3 x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$3 x^{3} - x^{2} + 6 x (3 x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Rewrite using the commutative property of multiplication.

$3 x^{3} - x^{2} + 6 \cdot 3 x \cdot x + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 x^{3} - x^{2} + 6 \cdot 3 (x \cdot x) + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Multiply $x$ by $x$ .

$3 x^{3} - x^{2} + 6 \cdot 3 x^{2} + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Multiply $6$ by $3$ .

$3 x^{3} - x^{2} + 18 x^{2} + 6 x \cdot - 1 + 9 (3 x) + 9 \cdot - 1$

Multiply $- 1$ by $6$ .

$3 x^{3} - x^{2} + 18 x^{2} - 6 x + 9 (3 x) + 9 \cdot - 1$

Multiply $3$ by $9$ .

$3 x^{3} - x^{2} + 18 x^{2} - 6 x + 27 x + 9 \cdot - 1$

Multiply $9$ by $- 1$ .

$3 x^{3} - x^{2} + 18 x^{2} - 6 x + 27 x - 9$

Simplify by adding terms.

Add $- x^{2}$ and $18 x^{2}$ .

$3 x^{3} + 17 x^{2} - 6 x + 27 x - 9$

Add $- 6 x$ and $27 x$ .

$3 x^{3} + 17 x^{2} + 21 x - 9$