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 $5$ .

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

Move $5$ to the left of $i$ .

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

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 $- 1$ .

$25 + 5 i + 5 i - 1$

$25 + 5 i + 5 i - 1$

Subtract $1$ from $25$ .

$24 + 5 i + 5 i$

Add $5 i$ and $5 i$ .

$24 + 10 i$

$24 + 10 i$

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