Factor completely:
X^3n+y^3n
Do I factor it as a cube?
Can't figure it out
this is the sum of two cubes:
(x^n)^3 + (y^n)^3
(x^n + y^n)(x^2n - x^n y^n + y^2n)
To factor the expression X^3n + y^3n completely, we can use the formula for factoring the sum of cubes. The formula states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2).
Applying this formula to our expression, we have:
X^3n + y^3n = (X^n)^3 + (y^n)^3
Now we can see that a = X^n and b = y^n, so we can rewrite the expression as:
(X^n)^3 + (y^n)^3 = (X^n + y^n)((X^n)^2 - (X^n)(y^n) + (y^n)^2)
Therefore, the expression X^3n + y^3n can be factored as (X^n + y^n)((X^n)^2 - (X^n)(y^n) + (y^n)^2).