Simplify (2+i)(2-i)

$(2 + i) (2 - i)$

Step 1

Expand $(2 + i) (2 - i)$ using the FOIL Method.

Apply the distributive property.

$2 (2 - i) + i (2 - i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- i) + i (2 - i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- i) + i \cdot 2 + i (- i)$

$2 \cdot 2 + 2 (- i) + i \cdot 2 + i (- i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (- i) + i \cdot 2 + i (- i)$

Multiply $- 1$ by $2$ .

$4 - 2 i + i \cdot 2 + i (- i)$

Move $2$ to the left of $i$ .

$4 - 2 i + 2 \cdot i + i (- i)$

Multiply $i (- i)$ .

Raise $i$ to the power of $1$ .

$4 - 2 i + 2 i - (i^{1} i)$

Raise $i$ to the power of $1$ .

$4 - 2 i + 2 i - (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 - 2 i + 2 i - i^{1 + 1}$

Add $1$ and $1$ .

$4 - 2 i + 2 i - i^{2}$

$4 - 2 i + 2 i - i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$4 - 2 i + 2 i - - 1$

Multiply $- 1$ by $- 1$ .

$4 - 2 i + 2 i + 1$

$4 - 2 i + 2 i + 1$

Add $4$ and $1$ .

$5 - 2 i + 2 i$

Add $- 2 i$ and $2 i$ .

$5 + 0$

Add $5$ and $0$ .

$5$

$5$

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