Simplify (2-yi)^2

${(2 - y i)}^{2}$

Rewrite ${(2 - y i)}^{2}$ as $(2 - y i) (2 - y i)$ .

$(2 - y i) (2 - y i)$

Expand $(2 - y i) (2 - y i)$ using the FOIL Method.

Apply the distributive property.

$2 (2 - y i) - y i (2 - y i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- y i) - y i (2 - y i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- y i) - y i \cdot 2 - y i (- y i)$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (- y i) - y i \cdot 2 - y i (- y i)$

Multiply $- 1$ by $2$ .

$4 - 2 (y i) - y i \cdot 2 - y i (- y i)$

Multiply $2$ by $- 1$ .

$4 - 2 y i - 2 y i - y i (- y i)$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$4 - 2 y i - 2 y i - (y \cdot y) i (- 1 i)$

Multiply $y$ by $y$ .

$4 - 2 y i - 2 y i - y^{2} i (- 1 i)$

Rewrite $- 1 i$ as $- i$ .

$4 - 2 y i - 2 y i - y^{2} i (- i)$

Multiply $- y^{2} i (- i)$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $y^{2}$ by $1$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Move $- 1$ to the left of $y^{2}$ .

$4 - 2 y i - 2 y i - 1 \cdot y^{2}$

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

$4 - 2 y i - 2 y i - y^{2}$

Subtract $2 y i$ from $- 2 y i$ .

$4 - 4 y i - y^{2}$

Simplify (2-yi)^2

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