Simplify (x+2i)^2

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

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

$(x + 2 i) (x + 2 i)$

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

Apply the distributive property.

$x (x + 2 i) + 2 i (x + 2 i)$

Apply the distributive property.

$x \cdot x + x (2 i) + 2 i (x + 2 i)$

Apply the distributive property.

$x \cdot x + x (2 i) + 2 i x + 2 i (2 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

$x^{2} + 2 \cdot x i + 2 i x + 2 i (2 i)$

Multiply $2 i (2 i)$ .

Multiply $2$ by $2$ .

$x^{2} + 2 x i + 2 i x + 4 i i$

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

$x^{2} + 2 x i + 2 i x + 4 (i^{1} i)$

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

$x^{2} + 2 x i + 2 i x + 4 (i^{1} i^{1})$

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

$x^{2} + 2 x i + 2 i x + 4 i^{1 + 1}$

Add $1$ and $1$ .

$x^{2} + 2 x i + 2 i x + 4 i^{2}$

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

$x^{2} + 2 x i + 2 i x + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$x^{2} + 2 x i + 2 i x - 4$

Add $2 x i$ and $2 i x$ .

Move $i$ .

$x^{2} + 2 x i + 2 x i - 4$

Add $2 x i$ and $2 x i$ .

$x^{2} + 4 x i - 4$