Find the term independent of x in the expansion of ( 1 + x +
x^-3)^7. Hint: Treat 1 + x as a single term.
( 1 + x + x^-3)^7
= ( (1 + x) + x^-3)^7
General Term = 7Cr (1+x)^(7-r) (x^-3)^r, where r is from 0 to
7
General Term of (1+x)^(7-r) = (7-r)Cq (x)^q
So, general term = 7Cr (7-r)Cq (x)^q (x^-3)^r
When r = 0, q = 0, thus independent term = 1
When r = 1, q = 3, thus independent term = 7C1 * 6C3 = 140
When r = 2, q = 6, thus independent term = 7C2 * 6C6 = 21
When r = 3 to 7, there's no independent term
Hence, term independent of x in the expansion of ( 1 + x +
x^-3)^7 is 1 + 140 + 21 = 162