Algebra Examples

(2 x - 4 y) (2 x + 4 y)

$(2 x - 4 y) (2 x + 4 y)$

Step 1

Expand

(2 x - 4 y) (2 x + 4 y)

$(2 x - 4 y) (2 x + 4 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 x (2 x + 4 y) - 4 y (2 x + 4 y)

$2 x (2 x + 4 y) - 4 y (2 x + 4 y)$

Step 1.2

Apply the distributive property.

2 x (2 x) + 2 x (4 y) - 4 y (2 x + 4 y)

$2 x (2 x) + 2 x (4 y) - 4 y (2 x + 4 y)$

Step 1.3

Apply the distributive property.

2 x (2 x) + 2 x (4 y) - 4 y (2 x) - 4 y (4 y)

$2 x (2 x) + 2 x (4 y) - 4 y (2 x) - 4 y (4 y)$

2 x (2 x) + 2 x (4 y) - 4 y (2 x) - 4 y (4 y)

$2 x (2 x) + 2 x (4 y) - 4 y (2 x) - 4 y (4 y)$

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 \cdot 2 x \cdot x + 2 x (4 y) - 4 y (2 x) - 4 y (4 y)

$2 \cdot 2 x \cdot x + 2 x (4 y) - 4 y (2 x) - 4 y (4 y)$

Step 2.1.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.1.2.1

Move

x

$x$ .

2 \cdot 2 (x \cdot x) + 2 x (4 y) - 4 y (2 x) - 4 y (4 y)

$2 \cdot 2 (x \cdot x) + 2 x (4 y) - 4 y (2 x) - 4 y (4 y)$

Step 2.1.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 2.1.3

Multiply

2

$2$ by

2

$2$ .

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

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

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

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

Step 2.1.5

Multiply

2

$2$ by

4

$4$ .

4 x^{2} + 8 x y - 4 y (2 x) - 4 y (4 y)

$4 x^{2} + 8 x y - 4 y (2 x) - 4 y (4 y)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

4 x^{2} + 8 x y - 4 \cdot 2 y x - 4 y (4 y)

$4 x^{2} + 8 x y - 4 \cdot 2 y x - 4 y (4 y)$

Step 2.1.7

Multiply

- 4

$- 4$ by

2

$2$ .

4 x^{2} + 8 x y - 8 y x - 4 y (4 y)

$4 x^{2} + 8 x y - 8 y x - 4 y (4 y)$

Step 2.1.8

Rewrite using the commutative property of multiplication.

4 x^{2} + 8 x y - 8 y x - 4 \cdot 4 y \cdot y

$4 x^{2} + 8 x y - 8 y x - 4 \cdot 4 y \cdot y$

Step 2.1.9

Multiply

y

$y$ by

y

$y$ by adding the exponents.

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Step 2.1.9.1

Move

y

$y$ .

4 x^{2} + 8 x y - 8 y x - 4 \cdot 4 (y \cdot y)

$4 x^{2} + 8 x y - 8 y x - 4 \cdot 4 (y \cdot y)$

Step 2.1.9.2

Multiply

y

$y$ by

y

$y$ .

4 x^{2} + 8 x y - 8 y x - 4 \cdot 4 y^{2}

$4 x^{2} + 8 x y - 8 y x - 4 \cdot 4 y^{2}$

4 x^{2} + 8 x y - 8 y x - 4 \cdot 4 y^{2}

$4 x^{2} + 8 x y - 8 y x - 4 \cdot 4 y^{2}$

Step 2.1.10

Multiply

- 4

$- 4$ by

4

$4$ .

4 x^{2} + 8 x y - 8 y x - 16 y^{2}

$4 x^{2} + 8 x y - 8 y x - 16 y^{2}$

4 x^{2} + 8 x y - 8 y x - 16 y^{2}

$4 x^{2} + 8 x y - 8 y x - 16 y^{2}$

Step 2.2

Subtract

8 y x

$8 y x$ from

8 x y

$8 x y$ .

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Step 2.2.1

Move

y

$y$ .

4 x^{2} + 8 x y - 8 x y - 16 y^{2}

$4 x^{2} + 8 x y - 8 x y - 16 y^{2}$

Step 2.2.2

Subtract

8 x y

$8 x y$ from

8 x y

$8 x y$ .

4 x^{2} + 0 - 16 y^{2}

$4 x^{2} + 0 - 16 y^{2}$

4 x^{2} + 0 - 16 y^{2}

$4 x^{2} + 0 - 16 y^{2}$

Step 2.3

Add

4 x^{2}

$4 x^{2}$ and

0

$0$ .

4 x^{2} - 16 y^{2}

$4 x^{2} - 16 y^{2}$

4 x^{2} - 16 y^{2}

$4 x^{2} - 16 y^{2}$