Question #a7e02

2 Answers
Nov 29, 2016

Actually, Josiah is correct

Explanation:

If x was equal to zero then the two expressions will be equal

If x=0

1) (-2x)^3=(-2*0)^3=0^3=0

2) -2x^3=-2*0^3=-2*0=0

But if it was any number else then the expressions won't be equal

If x=1

1) (-2*1)^3=(-2)^3=-8

2) -2*1^3=-2*1=-2

This is because the first expression was raised to the power of 3

(-2x)^3=(-2x)(-2x)(-2x)=(-2)(-2)(-2)(x)(x)(x)=-8x^3

And the second expression is

-2x^3

-8x^3 is not the same as -2x^3, so they will produce different values, except for x=0

Nov 30, 2016

They are the same if x=0 otherwise not the same

Explanation:

color(blue)("Consider: "(-2x)^3)

The brackets group together the -2 and the x

So the index (power) is applied to everything inside the bracket giving:

(-2x)xx(-2x)xx(-2x)

This is the same as:

(-2)^3xx(x)^3 = -8x^3

So " "color(blue)((-2x)^3=-8x^3)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(blue)("Consider: "-2x^3

In this case the -2 and the x are not 'locked' together other than by the operation of multiply. So we have:

(-2)xxx^3" "=" "-2x^3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Comparing the two")

It is stated that (-2x)^3=-2x^3

=> -8x^3=-2x^3

color(brown)("Consider the case "x!=0")

Divide both sies by x^3 giving

-8x^3=-2x^3" "->" " -8=-2 color(red)(larr" False")

"So for "x!=0:" " -8x^3!=-2x^3
..................................................................................................

color(brown)("Consider the case "x=0")

For x=0:" "-8x^3=02x^3

-8(0)^3=-2(0)^2

0=0" "color(red)(larr" True")

"So for "x=0:" " -8x^3=-2x^3