Simplify (2x+i)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

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

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

Move $i$ .

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

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

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