Simplify (x^2+x+9)(x-9)

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

Step 1

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

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

Step 2

Simplify terms.

Combine the opposite terms in $x^{2} x + x^{2} \cdot - 9 + x \cdot x + x \cdot - 9 + 9 x + 9 \cdot - 9$ .

Reorder the factors in the terms $x \cdot - 9$ and $9 x$ .

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

Add $- 9 x$ and $9 x$ .

$x^{2} x + x^{2} \cdot - 9 + x \cdot x + 0 + 9 \cdot - 9$

Add $x^{2} x + x^{2} \cdot - 9 + x \cdot x$ and $0$ .

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

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $- 9$ to the left of $x^{2}$ .

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

Multiply $x$ by $x$ .

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

Multiply $9$ by $- 9$ .

$x^{3} - 9 x^{2} + x^{2} - 81$

Add $- 9 x^{2}$ and $x^{2}$ .

$x^{3} - 8 x^{2} - 81$