Simplify (2-2x+x^2)(x+5)

$(2 - 2 x + x^{2}) (x + 5)$

Expand $(2 - 2 x + x^{2}) (x + 5)$ by multiplying each term in the first expression by each term in the second expression.

$2 x + 2 \cdot 5 - 2 x \cdot x - 2 x \cdot 5 + x^{2} x + x^{2} \cdot 5$

Simplify terms.

Simplify each term.

Multiply $2$ by $5$ .

$2 x + 10 - 2 x \cdot x - 2 x \cdot 5 + x^{2} x + x^{2} \cdot 5$

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

Move $x$ .

$2 x + 10 - 2 (x \cdot x) - 2 x \cdot 5 + x^{2} x + x^{2} \cdot 5$

Multiply $x$ by $x$ .

$2 x + 10 - 2 x^{2} - 2 x \cdot 5 + x^{2} x + x^{2} \cdot 5$

Multiply $5$ by $- 2$ .

$2 x + 10 - 2 x^{2} - 10 x + x^{2} x + x^{2} \cdot 5$

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

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

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

$2 x + 10 - 2 x^{2} - 10 x + x^{2} x^{1} + x^{2} \cdot 5$

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

$2 x + 10 - 2 x^{2} - 10 x + x^{2 + 1} + x^{2} \cdot 5$

Add $2$ and $1$ .

$2 x + 10 - 2 x^{2} - 10 x + x^{3} + x^{2} \cdot 5$

Move $5$ to the left of $x^{2}$ .

$2 x + 10 - 2 x^{2} - 10 x + x^{3} + 5 x^{2}$

Simplify by adding terms.

Subtract $10 x$ from $2 x$ .

$- 8 x + 10 - 2 x^{2} + x^{3} + 5 x^{2}$

Add $- 2 x^{2}$ and $5 x^{2}$ .

$- 8 x + 10 + x^{3} + 3 x^{2}$

Reorder.

Move $10$ .

$- 8 x + x^{3} + 3 x^{2} + 10$

Move $- 8 x$ .

$x^{3} + 3 x^{2} - 8 x + 10$