Simplify (8+i)^2

${(8 + i)}^{2}$

Step 1

Rewrite ${(8 + i)}^{2}$ as $(8 + i) (8 + i)$ .

$(8 + i) (8 + i)$

Step 2

Expand $(8 + i) (8 + i)$ using the FOIL Method.

Apply the distributive property.

$8 (8 + i) + i (8 + i)$

Apply the distributive property.

$8 \cdot 8 + 8 i + i (8 + i)$

Apply the distributive property.

$8 \cdot 8 + 8 i + i \cdot 8 + i i$

$8 \cdot 8 + 8 i + i \cdot 8 + i i$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $8$ .

$64 + 8 i + i \cdot 8 + i i$

Move $8$ to the left of $i$ .

$64 + 8 i + 8 \cdot i + i i$

Multiply $i i$ .

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

$64 + 8 i + 8 i + i^{1} i$

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

$64 + 8 i + 8 i + i^{1} i^{1}$

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

$64 + 8 i + 8 i + i^{1 + 1}$

Add $1$ and $1$ .

$64 + 8 i + 8 i + i^{2}$

$64 + 8 i + 8 i + i^{2}$

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

$64 + 8 i + 8 i - 1$

$64 + 8 i + 8 i - 1$

Subtract $1$ from $64$ .

$63 + 8 i + 8 i$

Add $8 i$ and $8 i$ .

$63 + 16 i$

$63 + 16 i$

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