Question

The side length, s, of a cube is x – 2y. If V = s3, what is the volume of the cube?
x3 – 6x2y + 12xy2 – 8y3
x3 + 6x2y + 12xy2 + 8y3
3x3 – 6x2y + 12xy2 – 24y3
3x3 + 6x2y + 12xy2 + 24y3

Answer 1

so volume = s^3 what mean (x-2y)^3

do you know formula (a-b)^3 = ?

Answer 2

no

Answer 3

ok than how you think what mean (a-b)^3 ?

Answer 4

idk im really confused

Answer 5

ok what mean 2^3 ?

Answer 6

8

Answer 7

or what mean 2^2 ?

Answer 8

yes but how you ve got this 8 ?

Answer 9

2^3 is 8 which means 2^2 is 4

Answer 10

yes this is true but how you get these 8 and 4 ?

Answer 11

not quite sure

Answer 12

2^2 = 2*2 = 4 bc. the exponent is 2 so this mean that you need multiply 2 time the 2 what is 2*2 = 4 and this way with 2^3 multiply 2 by 2 ,3 time

Answer 13

confused again

Answer 14

He's basically saying that 2^2 is 2*2
You multiply it by itself twice because the exponent is 2

When you do 2^3, since the exponent is 3, you multiply 2 by itself three times so
2*2*2 = 8
2^3 = 8

Does that make sense?

Answer 15

Now how does this relate to your question?
Your question involves a cube and they said that the side of the cube is (x-2y)

To find the volume of this cube, we have to use the formula they gave which is
V = s^3

Plug in what they gave us for s which is x-2y
And you get

V = (x-2y)^3

Now obviously we have to expand this and find out the correct answer.

Answer 16

So there's two ways to go about answering it

You don't know the formula for (a-b)^3
And I'll give that to you in a minute, would be handy to have it memorized

The other method is the longer way which you manually multiply it out and you have to use all that distributing rules you learned. And this is actually how they came up with the formula

(a-b)^3
= (a-b)(a-b)(a-b)
= (a^2 - 2ab + b^2)(a-b)
\(= \boxed{a^3 - 3a^2b + 3ab^2 - b^3}\)

I skipped a few steps but like that's how the formula is derived.

So like if you want you could do
(x-2y)(x-2y)(x-2y)
And you can multiply it all out

Or you can use the formula and x would be the a, and 2y is your b

Let me know if you have any questions or would like more clarification!