Algebra Examples

(2 x - 7) (2 x + 7)

$(2 x - 7) (2 x + 7)$

Step 1

Expand

(2 x - 7) (2 x + 7)

$(2 x - 7) (2 x + 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 x (2 x + 7) - 7 (2 x + 7)

$2 x (2 x + 7) - 7 (2 x + 7)$

Step 1.2

Apply the distributive property.

2 x (2 x) + 2 x \cdot 7 - 7 (2 x + 7)

$2 x (2 x) + 2 x \cdot 7 - 7 (2 x + 7)$

Step 1.3

Apply the distributive property.

2 x (2 x) + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7

$2 x (2 x) + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7$

2 x (2 x) + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7

$2 x (2 x) + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7$

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 7 - 7 (2 x) - 7 \cdot 7

$2 \cdot 2 x \cdot x + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7$

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 7 - 7 (2 x) - 7 \cdot 7

$2 \cdot 2 (x \cdot x) + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7$

Step 2.1.2.2

Multiply

x

$x$ by

x

$x$ .

2 \cdot 2 x^{2} + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7

$2 \cdot 2 x^{2} + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7$

2 \cdot 2 x^{2} + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7

$2 \cdot 2 x^{2} + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7$

Step 2.1.3

Multiply

2

$2$ by

2

$2$ .

4 x^{2} + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7

$4 x^{2} + 2 x \cdot 7 - 7 (2 x) - 7 \cdot 7$

Step 2.1.4

Multiply

7

$7$ by

2

$2$ .

4 x^{2} + 14 x - 7 (2 x) - 7 \cdot 7

$4 x^{2} + 14 x - 7 (2 x) - 7 \cdot 7$

Step 2.1.5

Multiply

2

$2$ by

- 7

$- 7$ .

4 x^{2} + 14 x - 14 x - 7 \cdot 7

$4 x^{2} + 14 x - 14 x - 7 \cdot 7$

Step 2.1.6

Multiply

- 7

$- 7$ by

7

$7$ .

4 x^{2} + 14 x - 14 x - 49

$4 x^{2} + 14 x - 14 x - 49$

4 x^{2} + 14 x - 14 x - 49

$4 x^{2} + 14 x - 14 x - 49$

Step 2.2

Subtract

14 x

$14 x$ from

14 x

$14 x$ .

4 x^{2} + 0 - 49

$4 x^{2} + 0 - 49$

Step 2.3

Add

4 x^{2}

$4 x^{2}$ and

0

$0$ .

4 x^{2} - 49

$4 x^{2} - 49$

4 x^{2} - 49

$4 x^{2} - 49$