Simplify x(x-2y)-(y-x)*2

$x (x - 2 y) - (y - x) \cdot 2$

Step 1

Simplify each term.

Apply the distributive property.

$x \cdot x + x (- 2 y) - (y - x) \cdot 2$

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

$x^{2} - 2 x y - (y - x) \cdot 2$

Apply the distributive property.

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

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

Move $2$ to the left of $x$ .

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

Step 2

Reorder $x^{2}$ and $- 2 x y$ .

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