Algebra Examples

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

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

Step 1

Expand

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

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

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Step 1.1

Apply the distributive property.

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

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

Step 1.2

Apply the distributive property.

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

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

Step 1.3

Apply the distributive property.

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

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

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

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

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

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

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

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

Step 2.1.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 2.1.3

Multiply

2

$2$ by

2

$2$ .

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

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

Step 2.1.4

Multiply

- 4

$- 4$ by

2

$2$ .

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

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

Step 2.1.5

Multiply

2

$2$ by

4

$4$ .

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

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

Step 2.1.6

Multiply

4

$4$ by

- 4

$- 4$ .

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

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

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

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

Step 2.2

Add

- 8 x

$- 8 x$ and

8 x

$8 x$ .

4 x^{2} + 0 - 16

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

Step 2.3

Add

4 x^{2}

$4 x^{2}$ and

0

$0$ .

4 x^{2} - 16

$4 x^{2} - 16$

4 x^{2} - 16

$4 x^{2} - 16$