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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $9$ to the left of $x$ .

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

Multiply $3$ by $- 3$ .

$x^{3} + 3 x^{2} + 9 x - 3 x^{2} - 9 x - 3 \cdot 9$

Multiply $- 3$ by $9$ .

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

Combine the opposite terms in $x^{3} + 3 x^{2} + 9 x - 3 x^{2} - 9 x - 27$ .

Subtract $3 x^{2}$ from $3 x^{2}$ .

$x^{3} + 9 x + 0 - 9 x - 27$

Add $x^{3} + 9 x$ and $0$ .

$x^{3} + 9 x - 9 x - 27$

Subtract $9 x$ from $9 x$ .

$x^{3} + 0 - 27$

Add $x^{3}$ and $0$ .

$x^{3} - 27$