Simplify (6+i)^2

${(6 + i)}^{2}$

Step 1

Rewrite ${(6 + i)}^{2}$ as $(6 + i) (6 + i)$ .

$(6 + i) (6 + i)$

Step 2

Expand $(6 + i) (6 + i)$ using the FOIL Method.

Apply the distributive property.

$6 (6 + i) + i (6 + i)$

Apply the distributive property.

$6 \cdot 6 + 6 i + i (6 + i)$

Apply the distributive property.

$6 \cdot 6 + 6 i + i \cdot 6 + i i$

$6 \cdot 6 + 6 i + i \cdot 6 + i i$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $6$ .

$36 + 6 i + i \cdot 6 + i i$

Move $6$ to the left of $i$ .

$36 + 6 i + 6 \cdot i + i i$

Multiply $i i$ .

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

$36 + 6 i + 6 i + i^{1} i$

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

$36 + 6 i + 6 i + i^{1} i^{1}$

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

$36 + 6 i + 6 i + i^{1 + 1}$

Add $1$ and $1$ .

$36 + 6 i + 6 i + i^{2}$

$36 + 6 i + 6 i + i^{2}$

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

$36 + 6 i + 6 i - 1$

$36 + 6 i + 6 i - 1$

Subtract $1$ from $36$ .

$35 + 6 i + 6 i$

Add $6 i$ and $6 i$ .

$35 + 12 i$

$35 + 12 i$

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