Thread: How to simplify x^3 - y^3 / x - y

How to simplify

x³ - y³ / x - y

Originally Posted by AaPa

How to simplify

x³ - y³ / x - y

look up the factoring pattern for the difference of cubes in your text or online.

You should know that:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
else you're not ready for this.

And your expression needs brackets: (x^3 - y^3) / (x - y)

I knew that x^3 - y^3 = (x - y)(x^2 + xy + y^2)

and

x^3 - y^3 / (x - y) = (x^2 + xy + y^2)

This is what I wanted to prove.

Originally Posted by AaPa

I knew that x^3 - y^3 = (x - y)(x^2 + xy + y^2)
and
x^3 - y^3 / (x - y) = (x^2 + xy + y^2)
This is what I wanted to prove.

Once more, be CAREFUL with brackets; should be:
(x^3 - y^3) / (x - y) = x^2 + xy + y^2

There is NOTHING to prove: simply cancel out the (x - y) terms: see Dobby's post...

Is there a way to find these factors of
x^3 - y^3
except try and error?

Google "difference of cubes".