Question

Can the cube of an integer be a negative number? Explain. I just want to make sure I am understanding. Here is what I believe.

Answer 1

Answer:

Yes, the cube of an integer can be a negative number.

Step-by-step explanation:

In essence, when we have a number cubed, say x, what we're doing is multiplying such number by itself three times:

$x^3=(x)(x)(x)$

Now, let's say that our number is a negative number, in this case -x. Let's take a look at what would happen:

$(x)(x)(x)\rightarrow(-x)(-x)(-x)\rightarrow(x^2)(-x)\rightarrow-x^3$

Prooving that, indeed, the cube of an integer can be a negative number.