Question

how to factor x^3 - y^3
show steps please

Answer 1

I always thought it was an identity and no steps ....just an answer\[x^3-y^3=(x-y)(x^2+xy+y^2)\]

Answer 2

the identity has to come from somewhere

Answer 3

Choose your god !

Answer 4

You could possibly use algebraic long division with the first factor known to get the second factor.

Answer 5

choose your god?
and im not sure how to go about doing long division on this

Answer 6

we can open \[(x+y)^3=x^3+3xy^2+3x^2y+y^3\]
\[(x+y)^3-3xy(x+y)=x^3+y^3\]
\[(x+y)((x+y)^2-3xy)=x^3+y^3\]
\[(x+y)(x^2+2xy-3xy+y^2)=x^3+y^3\]
\[(x+y)(x^2-xy+y^2)=x^3+y^3\]

Answer 7

this is for plus but you can do for -

Answer 8

Very nice work Jonask

Answer 9

alright thanks a lot

Answer 10

can you do -

Answer 11

x^3-y^3

Answer 12

(x-y)^3