Basic Math Examples

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

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

Step 1

Expand

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

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

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Step 1.1

Apply the distributive property.

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

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

Step 1.2

Apply the distributive property.

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

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

Step 1.3

Apply the distributive property.

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

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

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

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

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

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

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Step 2.1.1

Reorder the factors in the terms

2 x (2 y)

$2 x (2 y)$ and

- 2 y (2 x)

$- 2 y (2 x)$ .

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

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

Step 2.1.2

Subtract

2 \cdot 2 x y

$2 \cdot 2 x y$ from

2 \cdot 2 x y

$2 \cdot 2 x y$ .

2 x (2 x) + 0 - 2 y (2 y)

$2 x (2 x) + 0 - 2 y (2 y)$

Step 2.1.3

Add

2 x (2 x)

$2 x (2 x)$ and

0

$0$ .

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

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

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

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

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

Step 2.2.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.2.2.1

Move

x

$x$ .

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

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

Step 2.2.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 2.2.3

Multiply

2

$2$ by

2

$2$ .

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

$4 x^{2} - 2 y (2 y)$

Step 2.2.4

Rewrite using the commutative property of multiplication.

4 x^{2} - 2 \cdot 2 y \cdot y

$4 x^{2} - 2 \cdot 2 y \cdot y$

Step 2.2.5

Multiply

y

$y$ by

y

$y$ by adding the exponents.

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Step 2.2.5.1

Move

y

$y$ .

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

$4 x^{2} - 2 \cdot 2 (y \cdot y)$

Step 2.2.5.2

Multiply

y

$y$ by

y

$y$ .

4 x^{2} - 2 \cdot 2 y^{2}

$4 x^{2} - 2 \cdot 2 y^{2}$

4 x^{2} - 2 \cdot 2 y^{2}

$4 x^{2} - 2 \cdot 2 y^{2}$

Step 2.2.6

Multiply

- 2

$- 2$ by

2

$2$ .

4 x^{2} - 4 y^{2}

$4 x^{2} - 4 y^{2}$

4 x^{2} - 4 y^{2}

$4 x^{2} - 4 y^{2}$

4 x^{2} - 4 y^{2}

$4 x^{2} - 4 y^{2}$