which of the following expressions is equal to $2x^2 + 8$?

a. $(2x - 4i)(x + 2i)$

b. $(2x + 4i)(x + 2i)$

c. $(2x - 4i)(x - 2i)$

d. $(2x - 2i)(x + 6i)$

Question

which of the following expressions is equal to $2x^2 + 8$?

a. $(2x - 4i)(x + 2i)$

b. $(2x + 4i)(x + 2i)$

c. $(2x - 4i)(x - 2i)$

d. $(2x - 2i)(x + 6i)$

Accepted Answer

# Explanation:
## Step1: Expand Option A
Multiply $(2x - 4i)(x + 2i)$ using the distributive property (FOIL method):
$$
\begin{align*}
&2x \cdot x + 2x \cdot 2i - 4i \cdot x - 4i \cdot 2i\
=& 2x^2 + 4xi - 4xi - 8i^2
\end{align*}
$$
Since $i^2 = -1$, substitute:
$$
2x^2 + 4xi - 4xi - 8(-1) = 2x^2 + 8
$$
## Step2: Check Other Options (Optional, but for Confirmation)
- Option B: Expand $(2x + 4i)(x + 2i)$
$$
\begin{align*}
&2x \cdot x + 2x \cdot 2i + 4i \cdot x + 4i \cdot 2i\
=& 2x^2 + 4xi + 4xi + 8i^2\
=& 2x^2 + 8xi - 8
\end{align*}
$$
Not equal to $2x^2 + 8$.
- Option C: Expand $(2x - 4i)(x - 2i)$
$$
\begin{align*}
&2x \cdot x - 2x \cdot 2i - 4i \cdot x + 4i \cdot 2i\
=& 2x^2 - 4xi - 4xi + 8i^2\
=& 2x^2 - 8xi - 8
\end{align*}
$$
Not equal to $2x^2 + 8$.
- Option D: Expand $(2x - 2i)(x + 6i)$
$$
\begin{align*}
&2x \cdot x + 2x \cdot 6i - 2i \cdot x - 2i \cdot 6i\
=& 2x^2 + 12xi - 2xi - 12i^2\
=& 2x^2 + 10xi + 12
\end{align*}
$$
Not equal to $2x^2 + 8$.

# Answer:
A. $(2x - 4i)(x + 2i)$

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QUESTION IMAGE

Question

Explanation:

Step1: Expand Option A

Step2: Check Other Options (Optional, but for Confirmation)

Answer: