Algebra Examples

(2 a - b) (2 a + b)

$(2 a - b) (2 a + b)$

Step 1

Expand

(2 a - b) (2 a + b)

$(2 a - b) (2 a + b)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 a (2 a + b) - b (2 a + b)

$2 a (2 a + b) - b (2 a + b)$

Step 1.2

Apply the distributive property.

2 a (2 a) + 2 a b - b (2 a + b)

$2 a (2 a) + 2 a b - b (2 a + b)$

Step 1.3

Apply the distributive property.

2 a (2 a) + 2 a b - b (2 a) - b \cdot b

$2 a (2 a) + 2 a b - b (2 a) - b \cdot b$

2 a (2 a) + 2 a b - b (2 a) - b \cdot b

$2 a (2 a) + 2 a b - b (2 a) - b \cdot b$

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 a \cdot a + 2 a b - b (2 a) - b \cdot b

$2 \cdot 2 a \cdot a + 2 a b - b (2 a) - b \cdot b$

Step 2.1.2

Multiply

a

$a$ by

a

$a$ by adding the exponents.

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Step 2.1.2.1

Move

a

$a$ .

2 \cdot 2 (a \cdot a) + 2 a b - b (2 a) - b \cdot b

$2 \cdot 2 (a \cdot a) + 2 a b - b (2 a) - b \cdot b$

Step 2.1.2.2

Multiply

a

$a$ by

a

$a$ .

2 \cdot 2 a^{2} + 2 a b - b (2 a) - b \cdot b

$2 \cdot 2 a^{2} + 2 a b - b (2 a) - b \cdot b$

2 \cdot 2 a^{2} + 2 a b - b (2 a) - b \cdot b

$2 \cdot 2 a^{2} + 2 a b - b (2 a) - b \cdot b$

Step 2.1.3

Multiply

2

$2$ by

2

$2$ .

4 a^{2} + 2 a b - b (2 a) - b \cdot b

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

4 a^{2} + 2 a b - 1 \cdot 2 b a - b \cdot b

$4 a^{2} + 2 a b - 1 \cdot 2 b a - b \cdot b$

Step 2.1.5

Multiply

- 1

$- 1$ by

2

$2$ .

4 a^{2} + 2 a b - 2 b a - b \cdot b

$4 a^{2} + 2 a b - 2 b a - b \cdot b$

Step 2.1.6

Multiply

b

$b$ by

b

$b$ by adding the exponents.

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Step 2.1.6.1

Move

b

$b$ .

4 a^{2} + 2 a b - 2 b a - (b \cdot b)

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

Step 2.1.6.2

Multiply

b

$b$ by

b

$b$ .

4 a^{2} + 2 a b - 2 b a - b^{2}

$4 a^{2} + 2 a b - 2 b a - b^{2}$

4 a^{2} + 2 a b - 2 b a - b^{2}

$4 a^{2} + 2 a b - 2 b a - b^{2}$

4 a^{2} + 2 a b - 2 b a - b^{2}

$4 a^{2} + 2 a b - 2 b a - b^{2}$

Step 2.2

Subtract

2 b a

$2 b a$ from

2 a b

$2 a b$ .

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Step 2.2.1

Move

b

$b$ .

4 a^{2} + 2 a b - 2 a b - b^{2}

$4 a^{2} + 2 a b - 2 a b - b^{2}$

Step 2.2.2

Subtract

2 a b

$2 a b$ from

2 a b

$2 a b$ .

4 a^{2} + 0 - b^{2}

$4 a^{2} + 0 - b^{2}$

4 a^{2} + 0 - b^{2}

$4 a^{2} + 0 - b^{2}$

Step 2.3

Add

4 a^{2}

$4 a^{2}$ and

0

$0$ .

4 a^{2} - b^{2}

$4 a^{2} - b^{2}$

4 a^{2} - b^{2}

$4 a^{2} - b^{2}$