Simplify (2+i)^2-6(2+i)+9

${(2 + i)}^{2} - 6 (2 + i) + 9$

Simplify each term.

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

$(2 + i) (2 + i) - 6 (2 + i) + 9$

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

Apply the distributive property.

$2 (2 + i) + i (2 + i) - 6 (2 + i) + 9$

Apply the distributive property.

$2 \cdot 2 + 2 i + i (2 + i) - 6 (2 + i) + 9$

Apply the distributive property.

$2 \cdot 2 + 2 i + i \cdot 2 + i i - 6 (2 + i) + 9$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 i + i \cdot 2 + i i - 6 (2 + i) + 9$

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

$4 + 2 i + 2 \cdot i + i i - 6 (2 + i) + 9$

Multiply $i i$ .

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

$4 + 2 i + 2 i + i^{1} i - 6 (2 + i) + 9$

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

$4 + 2 i + 2 i + i^{1} i^{1} - 6 (2 + i) + 9$

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

$4 + 2 i + 2 i + i^{1 + 1} - 6 (2 + i) + 9$

Add $1$ and $1$ .

$4 + 2 i + 2 i + i^{2} - 6 (2 + i) + 9$

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

$4 + 2 i + 2 i - 1 - 6 (2 + i) + 9$

Subtract $1$ from $4$ .

$3 + 2 i + 2 i - 6 (2 + i) + 9$

Add $2 i$ and $2 i$ .

$3 + 4 i - 6 (2 + i) + 9$

Apply the distributive property.

$3 + 4 i - 6 \cdot 2 - 6 i + 9$

Multiply $- 6$ by $2$ .

$3 + 4 i - 12 - 6 i + 9$

Simplify by adding terms.

Subtract $12$ from $3$ .

$- 9 + 4 i - 6 i + 9$

Simplify by adding numbers.

Add $- 9$ and $9$ .

$0 + 4 i - 6 i$

Add $0$ and $4 i$ .

$4 i - 6 i$

Subtract $6 i$ from $4 i$ .

$- 2 i$

Simplify (2+i)^2-6(2+i)+9

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