SOLUTION: Find the constant term (x^0) in the expansion of: {{{ (1

SOLUTION: Find the constant term (x^0) in the expansion of: {{{ (1 - x^2 + x^3) (3x^2-(5/(7x^3)))^6 }}}

Question 1178563: Find the constant term (x^0) in the expansion of:

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

DO NOT expand the second factor completely and then multiply the result by the first factor. That is WAY too much work!

The second factor, when expanded, will contain terms of x^12, x^7, x^2, x^-3, x^-8, x^-13, and x^-18.

The only place where we will get a constant term (x^0) when that factor is multiplied by (1-x^2+x^3) is when the x^3 in the first factor is multiplied by the x^-3 term in the second factor.

The coefficient of the x^-3 term in the expanded second factor is

Then the constant term in the completely expanded expression is

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