Algebra Examples

(x + 5 i) (x - 5 i)

$(x + 5 i) (x - 5 i)$

Step 1

Expand

(x + 5 i) (x - 5 i)

$(x + 5 i) (x - 5 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

x (x - 5 i) + 5 i (x - 5 i)

$x (x - 5 i) + 5 i (x - 5 i)$

Step 1.2

Apply the distributive property.

x \cdot x + x (- 5 i) + 5 i (x - 5 i)

$x \cdot x + x (- 5 i) + 5 i (x - 5 i)$

Step 1.3

Apply the distributive property.

x \cdot x + x (- 5 i) + 5 i x + 5 i (- 5 i)

$x \cdot x + x (- 5 i) + 5 i x + 5 i (- 5 i)$

x \cdot x + x (- 5 i) + 5 i x + 5 i (- 5 i)

$x \cdot x + x (- 5 i) + 5 i x + 5 i (- 5 i)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

x \cdot x + x (- 5 i) + 5 i x + 5 i (- 5 i)

$x \cdot x + x (- 5 i) + 5 i x + 5 i (- 5 i)$ .

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Step 2.1.1

Reorder the factors in the terms

x (- 5 i)

$x (- 5 i)$ and

5 i x

$5 i x$ .

x \cdot x - 5 i x + 5 i x + 5 i (- 5 i)

$x \cdot x - 5 i x + 5 i x + 5 i (- 5 i)$

Step 2.1.2

Add

- 5 i x

$- 5 i x$ and

5 i x

$5 i x$ .

x \cdot x + 0 + 5 i (- 5 i)

$x \cdot x + 0 + 5 i (- 5 i)$

Step 2.1.3

Add

x \cdot x

$x \cdot x$ and

0

$0$ .

x \cdot x + 5 i (- 5 i)

$x \cdot x + 5 i (- 5 i)$

x \cdot x + 5 i (- 5 i)

$x \cdot x + 5 i (- 5 i)$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

x

$x$ by

x

$x$ .

x^{2} + 5 i (- 5 i)

$x^{2} + 5 i (- 5 i)$

Step 2.2.2

Multiply

5 i (- 5 i)

$5 i (- 5 i)$ .

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Step 2.2.2.1

Multiply

- 5

$- 5$ by

5

$5$ .

x^{2} - 25 i i

$x^{2} - 25 i i$

Step 2.2.2.2

Raise

i

$i$ to the power of

1

$1$ .

x^{2} - 25 (i^{1} i)

$x^{2} - 25 (i^{1} i)$

Step 2.2.2.3

Raise

i

$i$ to the power of

1

$1$ .

x^{2} - 25 (i^{1} i^{1})

$x^{2} - 25 (i^{1} i^{1})$

Step 2.2.2.4

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

x^{2} - 25 i^{1 + 1}

$x^{2} - 25 i^{1 + 1}$

Step 2.2.2.5

Add

1

$1$ and

1

$1$ .

x^{2} - 25 i^{2}

$x^{2} - 25 i^{2}$

x^{2} - 25 i^{2}

$x^{2} - 25 i^{2}$

Step 2.2.3

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

x^{2} - 25 \cdot - 1

$x^{2} - 25 \cdot - 1$

Step 2.2.4

Multiply

- 25

$- 25$ by

- 1

$- 1$ .

x^{2} + 25

$x^{2} + 25$

x^{2} + 25

$x^{2} + 25$

x^{2} + 25

$x^{2} + 25$

(x + 5 i) (x - 5 i)

$(x + 5 i) (x - 5 i)$

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

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