Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

Move $x$ .

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

Step 3.1.1.2

Multiply $x$ by $x$ .

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

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

Step 3.1.3

Multiply $2$ by $- 1$ .

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

Step 3.1.4

Rewrite using the commutative property of multiplication.

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

Step 3.1.5

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

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Step 3.1.5.1

Move $y$ .

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

Step 3.1.5.2

Multiply $y$ by $y$ .

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

Step 3.1.6

Multiply $2$ by $- 1$ .

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

Step 3.2

Add $- 2 x y$ and $2 y x$ .

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Step 3.2.1

Move $y$ .

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

Step 3.2.2

Add $- 2 x y$ and $2 x y$ .

$2 x^{2} + 0 - 2 y^{2}$

Step 3.3

Add $2 x^{2}$ and $0$ .

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