Simplify (5-i)^2

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

Step 1

Rewrite ${(5 - i)}^{2}$ as $(5 - i) (5 - i)$ .

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

Step 2

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 3

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

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

Multiply $- 1$ by $5$ .

$25 - 5 i - i \cdot 5 - i (- i)$

Multiply $5$ by $- 1$ .

$25 - 5 i - 5 i - i (- i)$

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

$25 - 5 i - 5 i + 1 i^{2}$

Multiply $i^{2}$ by $1$ .

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

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

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

$25 - 5 i - 5 i - 1$

$25 - 5 i - 5 i - 1$

Subtract $1$ from $25$ .

$24 - 5 i - 5 i$

Subtract $5 i$ from $- 5 i$ .

$24 - 10 i$

$24 - 10 i$

Related Questions