Question

Which of the following expressions is equal to -x2 -4

Answer 1

First, you can factor out the -. You then get

$-(x^{2}+2^{2})$.

It becomes clear that this is a difference of squares. So, you can factor this to be

$-(x-2i)(x+2i)$

Plugging in the - into one of the two factors gives you

$(-x-2i)(x-2i)$

Therefore, the answer is A.

Answer 2

The expression - x² - 4 is equal to the complex expression (- x - 2i)(x - 2i). Hence, option A is the right choice.

What are complex numbers?

Complex numbers are a combination of real numbers and imaginary numbers, which help us to represent the square roots of negative numbers.

It is of the form a + bi, where a and b are real constants, and i = √(-1).

How to solve the question?

In the question, we have been asked for an equal expression to -x² - 4.

The expression, - x² - 4, can be written as:

- x² - 4,

= - x² + (-1)(4),

= - x² + (i²)(2)² {Since, i = √(-1) ⇒ i² = -1},

= - x² + (2i)² {Since, aˣ.bˣ = (ab)ˣ},

= (2i)² - x² {Rearranging},

= (2i + x)(2i - x) {Since, a² - b² = (a + b)(a - b)},

= {-(-x - 2i)}{-(x - 2i)} {Rearranging},

= (- x - 2i)(x - 2i) {Simplifying}.

Thus, the expression - x² - 4 is equal to the complex expression (- x - 2i)(x - 2i). Hence, option A is the right choice.

Learn more about complex numbers at

https://brainly.com/question/11718993

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