Question

Determine whether the statement is true, false, or sometimes true.
1) If x and y are both integers, 1)
then (-x)3 = -x3
A) Sometimes true B) True C) False

Answer 1

If you mean
(-x)<sup>3</sub> = -x<sup>3</sub>

yes, that is always true

As a matter of fact, it is true for all odd exponents of n for
(-x)<sup>n</sub> = -x<sup>n</sub>
and false for all even numbers of n.

e.g. (-3)^3 = (-3)(-3)(-3) = -27
-3^3 = -(3)^3 = -(3)(3)(3) = -27
but

(-3)^4 = (-3)(-3)(-3)(-3) = +81
and -3^4 = -(3)(3)(3)(3) = -81

Answer 2

Let's try that again

If you mean
(-x)³ = -x³

yes, that is always true

As a matter of fact, it is true for all odd exponents of n for
(-x)n = -xn
and false for all even numbers of n.

e.g. (-3)^3 = (-3)(-3)(-3) = -27
-3^3 = -(3)^3 = -(3)(3)(3) = -27
but

(-3)^4 = (-3)(-3)(-3)(-3) = +81
and -3^4 = -(3)(3)(3)(3) = -81

Answer 3

Determine the nature of the solutions of the equations. 2t²-6t=0