Simplify (5-2i)(2+7i)-2i(3i)^2

$(5 - 2 i) (2 + 7 i) - 2 i {(3 i)}^{2}$

Simplify each term.

Expand $(5 - 2 i) (2 + 7 i)$ using the FOIL Method.

Apply the distributive property.

$5 (2 + 7 i) - 2 i (2 + 7 i) - 2 i {(3 i)}^{2}$

Apply the distributive property.

$5 \cdot 2 + 5 (7 i) - 2 i (2 + 7 i) - 2 i {(3 i)}^{2}$

Apply the distributive property.

$5 \cdot 2 + 5 (7 i) - 2 i \cdot 2 - 2 i (7 i) - 2 i {(3 i)}^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $2$ .

$10 + 5 (7 i) - 2 i \cdot 2 - 2 i (7 i) - 2 i {(3 i)}^{2}$

Multiply $7$ by $5$ .

$10 + 35 i - 2 i \cdot 2 - 2 i (7 i) - 2 i {(3 i)}^{2}$

Multiply $2$ by $- 2$ .

$10 + 35 i - 4 i - 2 i (7 i) - 2 i {(3 i)}^{2}$

Multiply $- 2 i (7 i)$ .

Multiply $7$ by $- 2$ .

$10 + 35 i - 4 i - 14 i i - 2 i {(3 i)}^{2}$

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

$10 + 35 i - 4 i - 14 (i^{1} i) - 2 i {(3 i)}^{2}$

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

$10 + 35 i - 4 i - 14 (i^{1} i^{1}) - 2 i {(3 i)}^{2}$

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

$10 + 35 i - 4 i - 14 i^{1 + 1} - 2 i {(3 i)}^{2}$

Add $1$ and $1$ .

$10 + 35 i - 4 i - 14 i^{2} - 2 i {(3 i)}^{2}$

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

$10 + 35 i - 4 i - 14 \cdot - 1 - 2 i {(3 i)}^{2}$

Multiply $- 14$ by $- 1$ .

$10 + 35 i - 4 i + 14 - 2 i {(3 i)}^{2}$

Add $10$ and $14$ .

$24 + 35 i - 4 i - 2 i {(3 i)}^{2}$

Subtract $4 i$ from $35 i$ .

$24 + 31 i - 2 i {(3 i)}^{2}$

Apply the product rule to $3 i$ .

$24 + 31 i - 2 i (3^{2} i^{2})$

Raise $3$ to the power of $2$ .

$24 + 31 i - 2 i (9 i^{2})$

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

$24 + 31 i - 2 i (9 \cdot - 1)$

Multiply $9$ by $- 1$ .

$24 + 31 i - 2 i \cdot - 9$

Multiply $- 9$ by $- 2$ .

$24 + 31 i + 18 i$

Add $31 i$ and $18 i$ .

$24 + 49 i$

Simplify (5-2i)(2+7i)-2i(3i)^2

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