how do you expand (x^3 - y^3) ?

Answer 1

There is nothing to expand. It is just x^3 - y^3.
Do you want to factor? Then you would use the formula for factoring the difference of two cubes.
x^3 - y^3 = (x-y)(x^2 + xy + y^2)

Answer 2

All of the correct answers expect you to remember a formula, which can be verified. But how to discover that formula?

If x = y then x^3 - y^3 = 0, so IF x^3 - y^3 can be factored then a reasonable answer is (x - y) * expression.

You can find the other factor by dividing x^3 - y^3 by x - y using "long division" [looks ugly because of the formatting!]

x^2 + x y + y^2
-------------
x - y ) x^3 - y^3
x^3 - x^2 y
--------------
x^2 y - y^3
x^2 y - x y^2
----------------
x y^2 - y^3
x y^2 - y^3
----------------
0

Another way is to equate

(x - y)( ax^2 + bxy + cy^2 ) and x^3 - y^3

and solve for a, b and c: it's obvious that a=1 and c = 1 then b = 1

It is useful to remember the formula, but in case you forgot you can apply some general principles to discover it!

Answer 3

The expression x^3 - y^3 is already "expanded." Usually "expand" is applied to a factored expression in order to reduce it to a sum of simple terms.

You most likely mean to factor the expression. The difference of two cubes is factored into:

(x - y)*(x^2 + x*y + y^2)

Notice that this equals:

x*(x^2 + x*y + y^2) - y*(x^2 + x*y + y^2)

The x^2*y and the x*y^2 terms cancel out. Thus, you're left with (x^3 - y^3).

If you don't mind complex coefficients, you can go farther than this an factor the quadratic. Then you get:

(x - y)*(x - (-1/2 - sqrt(3)/2)*i*y)*(x - (-1/2 + sqrt(3)/2)*i*y)

However, most likely you'll be safe just going with the answer with real coefficients:

(x - y)*(x^2 + x*y + y^2)

Answer 4

This is one way to expand your equation:
(x^(3/2)+y^(3/2)) (x^(3/2)-y^(3/2)) If you prefer using decimals, 1.5 could be substituted for 3/2. Hope this helps!

Answer 5

(x - y)*(x^2 + x*y + y^2)

Answer 6

(x^2*x)-(y^2*y)

Answer 7

(x-y)(x^2+xy+y^2)

Answer 8

x*x*x-y*y*y

Answer 9

(x-y)(x-y)(x-y) i think?