Algebra Examples

(2 x + 1) (2 x - 1)

$(2 x + 1) (2 x - 1)$

Step 1

Expand

(2 x + 1) (2 x - 1)

$(2 x + 1) (2 x - 1)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

2 x (2 x - 1) + 1 (2 x - 1)

$2 x (2 x - 1) + 1 (2 x - 1)$

Step 1.2

Apply the distributive property.

2 x (2 x) + 2 x \cdot - 1 + 1 (2 x - 1)

$2 x (2 x) + 2 x \cdot - 1 + 1 (2 x - 1)$

Step 1.3

Apply the distributive property.

2 x (2 x) + 2 x \cdot - 1 + 1 (2 x) + 1 \cdot - 1

$2 x (2 x) + 2 x \cdot - 1 + 1 (2 x) + 1 \cdot - 1$

2 x (2 x) + 2 x \cdot - 1 + 1 (2 x) + 1 \cdot - 1

$2 x (2 x) + 2 x \cdot - 1 + 1 (2 x) + 1 \cdot - 1$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in

2 x (2 x) + 2 x \cdot - 1 + 1 (2 x) + 1 \cdot - 1

$2 x (2 x) + 2 x \cdot - 1 + 1 (2 x) + 1 \cdot - 1$ .

Tap for more steps...

Step 2.1.1

Reorder the factors in the terms

2 x \cdot - 1

$2 x \cdot - 1$ and

1 (2 x)

$1 (2 x)$ .

2 x (2 x) - 1 \cdot 2 x + 1 \cdot 2 x + 1 \cdot - 1

$2 x (2 x) - 1 \cdot 2 x + 1 \cdot 2 x + 1 \cdot - 1$

Step 2.1.2

Add

- 1 \cdot 2 x

$- 1 \cdot 2 x$ and

1 \cdot 2 x

$1 \cdot 2 x$ .

2 x (2 x) + 0 + 1 \cdot - 1

$2 x (2 x) + 0 + 1 \cdot - 1$

Step 2.1.3

Add

2 x (2 x)

$2 x (2 x)$ and

0

$0$ .

2 x (2 x) + 1 \cdot - 1

$2 x (2 x) + 1 \cdot - 1$

2 x (2 x) + 1 \cdot - 1

$2 x (2 x) + 1 \cdot - 1$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Rewrite using the commutative property of multiplication.

2 \cdot 2 x \cdot x + 1 \cdot - 1

$2 \cdot 2 x \cdot x + 1 \cdot - 1$

Step 2.2.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

Tap for more steps...

Step 2.2.2.1

Move

x

$x$ .

2 \cdot 2 (x \cdot x) + 1 \cdot - 1

$2 \cdot 2 (x \cdot x) + 1 \cdot - 1$

Step 2.2.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 2.2.3

Multiply

2

$2$ by

2

$2$ .

4 x^{2} + 1 \cdot - 1

$4 x^{2} + 1 \cdot - 1$

Step 2.2.4

Multiply

- 1

$- 1$ by

1

$1$ .

4 x^{2} - 1

$4 x^{2} - 1$

4 x^{2} - 1

$4 x^{2} - 1$

4 x^{2} - 1

$4 x^{2} - 1$