Question
Which of the following is equivalent to −2i(3i + 4i)?(1 point)%0D%0AResponses%0D%0A%0D%0A−7i %0D%0Anegative 7 i%0D%0A%0D%0A6−8i%0D%0A6 minus 8 i%0D%0A%0D%0A14%0D%0A14%0D%0A%0D%0A−4i
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Answered by
GPT-4o mini
To simplify the expression \(-2i(3i + 4i)\), we first combine the terms inside the parentheses:
\[
3i + 4i = 7i
\]
Now, we can rewrite the expression as:
\[
-2i(7i)
\]
Next, we multiply:
\[
-2i \cdot 7i = -14i^2
\]
Since \(i^2 = -1\), we can substitute:
\[
-14i^2 = -14(-1) = 14
\]
So, the expression simplifies to:
\[
14
\]
The correct answer is \(14\).
\[
3i + 4i = 7i
\]
Now, we can rewrite the expression as:
\[
-2i(7i)
\]
Next, we multiply:
\[
-2i \cdot 7i = -14i^2
\]
Since \(i^2 = -1\), we can substitute:
\[
-14i^2 = -14(-1) = 14
\]
So, the expression simplifies to:
\[
14
\]
The correct answer is \(14\).
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