Use special products to expand and simplify: (x^3n-b^2m)^3show solution and explain the answer.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to expand the binomial using the formula such that:

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

You need to substitute `x^(3n)`  for x and `b^(2m)`  for y such that:

`(x^(3n)-b^(2m))^3 = (x^(3n))^3 - 3(x^(3n))^2*b^(2m) + 3x^(3n)*(b^(2m))^2 - (b^(2m))^3`

`(x^(3n)-b^(2m))^3 = (x^(9n)) - 3(x^(6n))*b^(2m) + 3x^(3n)*(b^(4m)) - (b^(6m))`

Hence, expanding the binomial yields `(x^(3n)-b^(2m))^3 = (x^(9n)) - 3(x^(6n))*b^(2m) + 3x^(3n)*(b^(4m)) - (b^(6m)).`