Algebra Examples

(a - b) (a + b)

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

Step 1

Expand

(a - b) (a + b)

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

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Step 1.1

Apply the distributive property.

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

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

Step 1.2

Apply the distributive property.

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

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

Step 1.3

Apply the distributive property.

a \cdot a + a b - b a - b \cdot b

$a \cdot a + a b - b a - b \cdot b$

a \cdot a + a b - b a - b \cdot b

$a \cdot a + a b - b a - b \cdot b$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

a \cdot a + a b - b a - b \cdot b

$a \cdot a + a b - b a - b \cdot b$ .

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Step 2.1.1

Reorder the factors in the terms

a b

$a b$ and

- b a

$- b a$ .

a \cdot a + a b - a b - b \cdot b

$a \cdot a + a b - a b - b \cdot b$

Step 2.1.2

Subtract

a b

$a b$ from

a b

$a b$ .

a \cdot a + 0 - b \cdot b

$a \cdot a + 0 - b \cdot b$

Step 2.1.3

Add

a \cdot a

$a \cdot a$ and

0

$0$ .

a \cdot a - b \cdot b

$a \cdot a - b \cdot b$

a \cdot a - b \cdot b

$a \cdot a - b \cdot b$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

a

$a$ by

a

$a$ .

a^{2} - b \cdot b

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

Step 2.2.2

Multiply

b

$b$ by

b

$b$ by adding the exponents.

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Step 2.2.2.1

Move

b

$b$ .

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

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

Step 2.2.2.2

Multiply

b

$b$ by

b

$b$ .

a^{2} - b^{2}

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

a^{2} - b^{2}

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

a^{2} - b^{2}

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

a^{2} - b^{2}

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

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$