Question

Factor the difference of 2 cubes: 54x^3-250y^3

Answer 1

Do you know the rule for factoring difference of cubes?

Answer 2

a^3-b^3= (a-b)(a^2+ab+b^2)

Answer 3

\[\huge a^3 – b^3 = (a – b)(a^2 + ab + b^2)\]

Answer 4

http://en.wikipedia.org/wiki/Factorization#Sum.2Fdifference_of_two_cubes

Answer 5

yes. So just factor out the common factor - there is a GCF of 2 - and then you should have a difference of cubes to just plug and chug in that formula.

Answer 6

I hate math and I'm not good at it at all. I just don't have a "math brain." i know the GCF is 2... but I dont know what to do after that.. 2(27x^3-125y^3) ??

Answer 7

Note: \(\large 54=3^3\times 2\) and \(\large 250=5^3\times 2\). So there are some nice cubes in there with a common factor.

Answer 8

2x(3x^2-5x^2) ?

Answer 9

If you multiply that 2 back through what you did, do you get what you started with?

Answer 10

"factoring out" just means you take that common factor (2 is the GCF because it's the biggest number that is a factor of both 54 and 250) and "divide it out" of each term, so that it comes out side the ( )'s.

Answer 11

\[54x^3-250y^3=2(?x^3-?y^3)\]

Answer 12

Close:

\(\Large 2((3x)^3 - (5y)^3)\), then set \(a=3x\) and \(b=5x\) in our formula above

Answer 13

(3x-5x)(6x+8x+25x) ?

Answer 14

You got it!

I should have said set \( a=3x\) and \(b=5y \) in our formula:
\((3x-5y)(9x^2+15xy+25y^2) \), which is as simple as we can get.

That's it!

Answer 15

ok, thank you @ybarrap wouldnt it be (3x-5y)(9x+15xy+25x)

Answer 16

i mean (3x-5y)(9x+15x+25y)

Answer 17

ah, i keep missing one: (3x-5y)(9x+15xy+25y)

Answer 18

The \(9x\) should be \(9x^2 \) because when we set \(a=3x\) and then square it, we get \((3x)^2=9x^2\), same thing for \(25x\): \(b^2=(5y)^2=25y^2 \) and in the middle, instead of 15x, you should have for \(ab=(3x)(5y)=15xy\)

Answer 19

its saying that's not correct @ybarrap

Answer 20

did you multiply the whole thing times 2? Remember this was our common factor between 54 and 250 that allowed us to set a=3x and b=5y:

\(2(3x-5y)(9x^2+15xy+25y^2)\)

Answer 21

no. so its... (6x-10y)(18x^2+30xy+50y^2) ?

Answer 22

\(2(3x-5y)(9x^2+15xy+25y^2)=(6x-10y)(9x^2+15xy+25y^2)\)

Remember, for example, 2*(5)(6) = (2*5)(6) or (5)(2*6) not (2*5)(2*6), which can easily verify with a calculator

Answer 23

Does this make sense?

Answer 24

yes, it said that was wrong too. it was looking for 2(3x-5y)(9x^2+15xy+25y^2)

Answer 25

That's exactly what I have above

Answer 26

i put in the (6x-10y) one. Thank you though