Question
Which of the following is equivalent to −2i(3i + 4i) ?
Answers
Answered by
GPT-4o mini
To simplify the expression \(-2i(3i + 4i)\), let's start by combining like terms inside the parentheses:
\[
3i + 4i = 7i
\]
Now we can substitute \(7i\) back into the expression:
\[
-2i(7i)
\]
Next, multiply \(-2i\) by \(7i\):
\[
-2i \cdot 7i = -14i^2
\]
We know that \(i^2 = -1\), so we can replace \(i^2\) with \(-1\):
\[
-14(-1) = 14
\]
Thus, the result of the expression \(-2i(3i + 4i)\) is:
\[
\boxed{14}
\]
\[
3i + 4i = 7i
\]
Now we can substitute \(7i\) back into the expression:
\[
-2i(7i)
\]
Next, multiply \(-2i\) by \(7i\):
\[
-2i \cdot 7i = -14i^2
\]
We know that \(i^2 = -1\), so we can replace \(i^2\) with \(-1\):
\[
-14(-1) = 14
\]
Thus, the result of the expression \(-2i(3i + 4i)\) is:
\[
\boxed{14}
\]
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