Question

Which of the following is equivalent to −2i(3i + 4i) ?(1 point)
Responses

−7i
negative 7 i

14
14

−4i
negative 4 i

6−8i

Answer 1

To simplify the expression \( -2i(3i + 4i) \), we first combine the terms inside the parentheses:

\[
3i + 4i = 7i
\]

Now, substitute this back into the expression:

\[
-2i(7i)
\]

Next, we multiply:

\[
-2i \cdot 7i = -14i^2
\]

Since \( i^2 = -1 \), we substitute \( -1 \) for \( i^2 \):

\[
-14i^2 = -14(-1) = 14
\]

Thus, the expression simplifies to:

\[
14
\]

So the equivalent expression is \( \boxed{14} \).