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

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

Step 1

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

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

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 $1$ .

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 2$ by $2$ .

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

Multiply $2$ by $1$ .

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

Simplify by adding terms.

Combine the opposite terms in $x^{3} - 2 x^{2} + x + 2 x^{2} - 4 x + 2$ .

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

$x^{3} + x + 0 - 4 x + 2$

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

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

Subtract $4 x$ from $x$ .

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