Question

factorize x^3 + 216y^3 + 82^3 - 36xyz

Answer 1

Answer:

Assuming that 82^3 is actually 8z^3, then the factorization is:

(x + 6 y + 2 z) (x^2 - 6 x y - 2 x z + 36 y^2 - 12 y z + 4 z^2)

Step-by-step explanation:

Given that (a+b)(a^2-ab+b^2) = a^3 - b^3, we can expand on that idea and see that (a+b+c)(a^2+b^2+c^2-ab-bc-ac) = a^3+b^3+c^3-3abc.

Defining: a = x, b = 6y, c = 2z, we arrive at the factorization given above.