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

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spock7 | Student, Undergraduate | Honors

Posted April 27, 2012 at 1:16 PM via web

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Use special products to expand and simplify: (x^3n-b^2m)^3

show solution and explain the answer.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 27, 2012 at 1:29 PM (Answer #1)

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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)).`

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