Find the Product (x-y)(2x-y)

$(x - y) (2 x - y)$

Step 1

Expand $(x - y) (2 x - y)$ using the FOIL Method.

Apply the distributive property.

$x (2 x - y) - y (2 x - y)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $2$ .

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

Rewrite using the commutative property of multiplication.

$2 x^{2} - x y - 2 y x - 1 \cdot - 1 y \cdot y$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

$2 x^{2} - x y - 2 y x - 1 \cdot - 1 y^{2}$

Multiply $- 1$ by $- 1$ .

$2 x^{2} - x y - 2 y x + 1 y^{2}$

Multiply $y^{2}$ by $1$ .

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

Subtract $2 y x$ from $- x y$ .

Move $y$ .

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

Subtract $2 x y$ from $- x y$ .

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