Asked by yeslian c
Which of the following shows the expression (4i − 3)(−2i + 2)
completely simplified using the Distributive Property?(1 point)
Responses
−12
negative 12
2+14i
2 plus 14 i
−8i2+14i−6
negative 8 i squared plus 14 i minus 6
14+2i
completely simplified using the Distributive Property?(1 point)
Responses
−12
negative 12
2+14i
2 plus 14 i
−8i2+14i−6
negative 8 i squared plus 14 i minus 6
14+2i
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To simplify the expression \((4i - 3)(-2i + 2)\) using the Distributive Property (also known as FOIL for two binomials), we follow these steps:
1. **Distribute each term in the first binomial by each term in the second binomial**:
\(4i \cdot -2i = -8i^2\)
\(4i \cdot 2 = 8i\)
\(-3 \cdot -2i = 6i\)
\(-3 \cdot 2 = -6\)
2. **Combine all the products**:
\(-8i^2 + 8i + 6i - 6\)
Combine like terms:
- The imaginary parts: \(8i + 6i = 14i\)
So, we get:
\(-8i^2 + 14i - 6\)
Therefore, the completely simplified expression is:
**−8i^2 + 14i − 6**
This corresponds to the option:
**negative 8 i squared plus 14 i minus 6**.
1. **Distribute each term in the first binomial by each term in the second binomial**:
\(4i \cdot -2i = -8i^2\)
\(4i \cdot 2 = 8i\)
\(-3 \cdot -2i = 6i\)
\(-3 \cdot 2 = -6\)
2. **Combine all the products**:
\(-8i^2 + 8i + 6i - 6\)
Combine like terms:
- The imaginary parts: \(8i + 6i = 14i\)
So, we get:
\(-8i^2 + 14i - 6\)
Therefore, the completely simplified expression is:
**−8i^2 + 14i − 6**
This corresponds to the option:
**negative 8 i squared plus 14 i minus 6**.
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