Basic Math Examples

(a + 1) (a - 1)

$(a + 1) (a - 1)$

Step 1

Expand

(a + 1) (a - 1)

$(a + 1) (a - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

a (a - 1) + 1 (a - 1)

$a (a - 1) + 1 (a - 1)$

Step 1.2

Apply the distributive property.

a \cdot a + a \cdot - 1 + 1 (a - 1)

$a \cdot a + a \cdot - 1 + 1 (a - 1)$

Step 1.3

Apply the distributive property.

a \cdot a + a \cdot - 1 + 1 a + 1 \cdot - 1

$a \cdot a + a \cdot - 1 + 1 a + 1 \cdot - 1$

a \cdot a + a \cdot - 1 + 1 a + 1 \cdot - 1

$a \cdot a + a \cdot - 1 + 1 a + 1 \cdot - 1$

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

Multiply

a

$a$ by

a

$a$ .

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

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

Step 2.1.2

Move

- 1

$- 1$ to the left of

a

$a$ .

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

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

Step 2.1.3

Rewrite

- 1 a

$- 1 a$ as

- a

$- a$ .

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

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

Step 2.1.4

Multiply

a

$a$ by

1

$1$ .

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

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

Step 2.1.5

Multiply

- 1

$- 1$ by

1

$1$ .

a^{2} - a + a - 1

$a^{2} - a + a - 1$

a^{2} - a + a - 1

$a^{2} - a + a - 1$

Step 2.2

Add

- a

$- a$ and

a

$a$ .

a^{2} + 0 - 1

$a^{2} + 0 - 1$

Step 2.3

Add

a^{2}

$a^{2}$ and

0

$0$ .

a^{2} - 1

$a^{2} - 1$

a^{2} - 1

$a^{2} - 1$

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

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