Simplify (2+5i)(-1+5i)

$(2 + 5 i) (- 1 + 5 i)$

Step 1

Expand $(2 + 5 i) (- 1 + 5 i)$ using the FOIL Method.

Apply the distributive property.

$2 (- 1 + 5 i) + 5 i (- 1 + 5 i)$

Apply the distributive property.

$2 \cdot - 1 + 2 (5 i) + 5 i (- 1 + 5 i)$

Apply the distributive property.

$2 \cdot - 1 + 2 (5 i) + 5 i \cdot - 1 + 5 i (5 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $- 1$ .

$- 2 + 2 (5 i) + 5 i \cdot - 1 + 5 i (5 i)$

Multiply $5$ by $2$ .

$- 2 + 10 i + 5 i \cdot - 1 + 5 i (5 i)$

Multiply $- 1$ by $5$ .

$- 2 + 10 i - 5 i + 5 i (5 i)$

Multiply $5 i (5 i)$ .

Multiply $5$ by $5$ .

$- 2 + 10 i - 5 i + 25 i i$

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

$- 2 + 10 i - 5 i + 25 (i^{1} i)$

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

$- 2 + 10 i - 5 i + 25 (i^{1} i^{1})$

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

$- 2 + 10 i - 5 i + 25 i^{1 + 1}$

Add $1$ and $1$ .

$- 2 + 10 i - 5 i + 25 i^{2}$

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

$- 2 + 10 i - 5 i + 25 \cdot - 1$

Multiply $25$ by $- 1$ .

$- 2 + 10 i - 5 i - 25$

Subtract $25$ from $- 2$ .

$- 27 + 10 i - 5 i$

Subtract $5 i$ from $10 i$ .

$- 27 + 5 i$