Question

I have 5 questions that involve factoring the difference and sum of cubes. Can anyone please help me out with them?

This is the first one:
Choose one of the factors of 24x^6 – 1029y^3

3

2x^2 – 7y

4x^4 + 14x^2y + 49y^2

All of the above

Answer 1

Alright, so you just find CGF, and ... I don't quite understand the setting the numbers up as cubes.

Answer 2

Where do you get the 4x^4 from? ... and all the other numbers in that factor from?

Answer 3

@etenraku1

Answer 4

one second.

Answer 5

Alright.

Answer 6

Choose one of the factors of 5x^3 – 135

5

x – 3

x^2 + 3x + 9

All of the above

This is the 3rd problem, the second one is confusing, however this one is similar to the first. I'm going to try and do what you just did.

Answer 7

Here's a more detailed #1

Answer 8

I'm stuck at 5(x^3 - 27)

Answer 9

Try cubing small number until you pass 27. Like 1^3 = 1, 2^3 = 8, 3^3 = ...

Like that.

Answer 10

Ok. 3^3 = 27.

Answer 11

now is it 5(x^2 - 3^3)

Answer 12

correct! Now what's your A and B, if

(A^3 - B^3) = (A-B)(A^2 + AB + B^2)

Answer 13

a = x
b = 3?

Answer 14

Exactly! Now you just plug it into the formula. That's it.

Answer 15

(x - 3)(x^2 + x3 + 3^2)

Answer 16

That is correct.

Answer 17

how would I write x3?

Answer 18

3x. Typically in the business we put the number first.

Answer 19

alright... I have 1 more ima try on my own... I'll mention you when I'm done..

Answer 20

OK

Answer 21

x^3 - 348 is the question.

Answer 22

343*

Answer 23

(x - 7)(x^2 + 7x + 7^2)

Answer 24

Exactly. Now the formula changes if there is a plus between the two cubes, but in this case it is a '-'.

Good job!

Answer 25

Holy crap, these are easy! :D

Answer 26

@etenraku1 I read the question wrong. It was x^3 + 343.

Answer 27

Does this just mean the formulas signs get flipped?

Answer 28

Not quite flipped. For differences, only the first is negative. For sums, only the second is negative.

Answer 29

So the final equation would be (x + 7)(x^2 - 7x - 7^2)?

Answer 30

last sign is positive. Otherwise, yes!

Answer 31

Ok, (x+7)(x^2 - 7x + 7^2)

Answer 32

Correct!

Answer 33

Awesome! Thank you so much!

Answer 34

Err Wait.

Answer 35

How do I do it if there is no GCF and the question looks like this: 1331x^3 – 8y^
3

Answer 36

My pleasure.

Answer 37

Like this. Just think of the GCF as 1.

Answer 38

Same way as the other ones... cool!

Answer 39

Alright, I think that's it. Thanks again!