factoring in algebra?

Question

what does x^6-y^6
end up to be i used a calculator to do this but
my answer is still incorrect.
x^6+x^3-y^6

and how do you type in
exponets that are like this n-1?will it ben^-1^?

Answer 1

x^6 - y^6 = (x^3-y^3)(x^3+y^3)
= (x-y) (x^2+xy +y^2)(x+y)(x^2 - xy + y^2)

two factoring method were used, square of the difference and sum and difference of a cube

n^(-1) meaning n raise to the exponent negative one

Answer 2

Well since (z^a)^2 = z^(2a), we can look at the problem as the difference of sqares:

(x^6) - (y^6)
[(x^3)^2] - [(y^3)^2]

Since A² - B&sup^2; = (A+B)(A-B)...
(x³ + y³)(x³ - y³)

Leaving us with two factors, one of which is the sum of cubes, the other is the difference of cubes. We know that the sum of two cubes always factors like this:
a³ + b³ = (a+b)(a² - ab + b²)
and the difference will always factor like this:
a³ - b³ = (a-b)(a² + ab + b²)

We plug in the right variables, giving us...
(x+y)(x² - xy + y²)(x-y)(x² + xy + y²).

As for showing exponents in type (without using a special math program) is to use a lot of brackets. For example,
n^(-1)
x^(n-1)

Answer 3

this is the diff of 2 squares
(x^3-y^3)(x^3+y^3)

The sum and diff of cubes are also factorable using a special formula you can look up.

x³ - y³ = (x-y)(x² + xy + y²)
x³ + y³ = (x+y)(x² - xy + y²)




x^(n-1)
use parenthesis

Answer 4

(x^3+y^3)(x^3-y^3)