Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Rewrite using the commutative property of multiplication.

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

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

Step 2.1.5

Multiply $- 1$ by $2$ .

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

Step 2.1.6

Rewrite using the commutative property of multiplication.

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

Step 2.1.7

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

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Step 2.1.7.1

Move $y$ .

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

Step 2.1.7.2

Multiply $y$ by $y$ .

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

Step 2.1.8

Multiply $- 1$ by $- 1$ .

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

Step 2.1.9

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

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

Step 2.2

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

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Step 2.2.1

Move $y$ .

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

Step 2.2.2

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

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