Simplify (5-i)(5+i)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$5 \cdot 5 + 5 i - i \cdot 5 - i i$

$5 \cdot 5 + 5 i - i \cdot 5 - i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

$25 + 5 i - i \cdot 5 - i i$

Multiply $5$ by $- 1$ .

$25 + 5 i - 5 i - i i$

Multiply $- i i$ .

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

$25 + 5 i - 5 i - (i^{1} i)$

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

$25 + 5 i - 5 i - (i^{1} i^{1})$

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

$25 + 5 i - 5 i - i^{1 + 1}$

Add $1$ and $1$ .

$25 + 5 i - 5 i - i^{2}$

$25 + 5 i - 5 i - i^{2}$

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

$25 + 5 i - 5 i - - 1$

Multiply $- 1$ by $- 1$ .

$25 + 5 i - 5 i + 1$

$25 + 5 i - 5 i + 1$

Add $25$ and $1$ .

$26 + 5 i - 5 i$

Subtract $5 i$ from $5 i$ .

$26 + 0$

Add $26$ and $0$ .

$26$

$26$

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