X ki power6 - y ki power 6 factorise

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

(x^3+3x^2y+3xy^2+y^3)*(x^3-x^2y+3xy^2-y^3)

ummm

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

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

To factorize the expression X^6 - Y^6, we can use the difference of squares formula and the difference of cubes formula.

Step 1: Apply the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b). In our case, a = X^2 and b = Y^2. Thus, we can rewrite the expression as (X^2 + Y^2)(X^4 - X^2Y^2 + Y^4).

Step 2: Apply the difference of cubes formula, which states that a^3 - b^3 can be factored as (a - b)(a^2 + ab + b^2). In our case, a = X^2 and b = Y^2. Thus, we can rewrite the first term (X^2 + Y^2) as [(X^2)^3 - (Y^2)^3] and factorize it as (X^2 - Y^2)(X^4 + X^2Y^2 + Y^4).

Combining the factorizations from Step 1 and Step 2, we get the final factorization:

X^6 - Y^6 = (X^2 - Y^2)(X^4 + X^2Y^2 + Y^4)