Question

how can you know the sum and difference of 2 cubes are being factored ?

Answer 1

what do you mean, "how can you know"?
If you have a sum of 2 cubes, or a difference of two cubes, it can always be factored.

Answer 2

i cant understand it .. this the the question ... know how the sum and difference of 2 cubes are being factored ..

Answer 3

do you have a problem you are trying to work out?
the two formulas you need to know are:
\[x^3-y^3 = (x-y)(x^2+xy+y^2)\]
and
\[x^3+y^3 = (x+y)(x^2-xy+y^2)\]

Answer 4

none .. just a question :/ math is hard for me :'(

Answer 5

alright, well here is an example:
\[x^3-125\]
Lets say you want to factor that. First you would need to notice that:
\[125 = 5^3\]
so we can re-write the question like this:
\[x^3-125 \Rightarrow x^3-5^3\]
Then, you should be thinking, "this is a difference of 2 cubes, i need to use that formula!"
So you look through your note and find the formula:
\[x^3-y^3 = (x-y)(x^2+xy+y^2)\]
but how do you use it?
put the left sides of the equation close to each other:
\[x^3-y^3\]
\[x^3-5^3\]
it looks like the 'x' stayed the same, but the y changed to a 5. So in the long expression:
\[(x-y)(x^2+xy+y^2)\]
change all the y's to 5's, and simplify if you can:
\[(x-5)(x^2+x(5)+5^2) = (x-5)(x^2+5x+25)\]
and then you are done :) so the answer would be:
\[x^3-5^3 = (x-5)(x^2+5x+25)\]
That is how you factor a difference of 2 cubes.

Answer 6

thanks to you .... thanks for your help im so very happy :) thank you and god bless more answer to come :) peace ....