Binomial Theorem

Question

Find the term independent of x in the expansion of (1+x+x-3)7 after the expansion is performed. Note that the answer is 141.

Answer 1

-> I misread your expression, but it looks like the other guy figured out that the -3 was an exponent.

Answer 2

By Binomial expansion

[1+(x + x^-3)]⁷ = 1 + 7(x + x^-3) + 21(x + x^-3)² + 35(x + x^-3)³ + 35(x + x^-3)⁴ + 21(x + x^-3)⁵ + 35(x + x^-3)⁶ + (x+x^-3)⁷

The 1 and 35(x + x^-3)⁴ have terms without x.

35[x⁴ + 4x³(x^-3)+6x²(x^-6)+4x²(x^-9)+x^-12]

= 35(x⁴+ 4 + ....)

The term without x = 35*4 = 140

140 + 1 = 141