Simplify (x+9)(x^2-4x+1)

$(x + 9) (x^{2} - 4 x + 1)$

Step 1

Expand $(x + 9) (x^{2} - 4 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (- 4 x) + x \cdot 1 + 9 x^{2} + 9 (- 4 x) + 9 \cdot 1$

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 $1$ .

$x^{1} x^{2} + x (- 4 x) + x \cdot 1 + 9 x^{2} + 9 (- 4 x) + 9 \cdot 1$

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

$x^{1 + 2} + x (- 4 x) + x \cdot 1 + 9 x^{2} + 9 (- 4 x) + 9 \cdot 1$

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 4$ by $9$ .

$x^{3} - 4 x^{2} + x + 9 x^{2} - 36 x + 9 \cdot 1$

Multiply $9$ by $1$ .

$x^{3} - 4 x^{2} + x + 9 x^{2} - 36 x + 9$

Simplify by adding terms.

Add $- 4 x^{2}$ and $9 x^{2}$ .

$x^{3} + 5 x^{2} + x - 36 x + 9$

Subtract $36 x$ from $x$ .

$x^{3} + 5 x^{2} - 35 x + 9$