how may terms are there in the expansion (1+(x)+(x^2)+(x^3))^16???

1) 49
2) 48
3) 16
4) 60

• Number of terms in expansion of (1+(x)+(x^2)+(x^3)+ .... + (x^n))^m = mn+1.
  Therefore, here m = 16, n=3. mn+1 = 49
• 10 years agoHelpfull: Yes(2) No(0)
• Answer = 60 (Option 4)
  (a+b) ^ 2 = 3 terms
  (a+b) ^ 3 = 4 terms
  
  (a+b) ^ 16 = 17 terms... (1)
  This repeats thrice as we have 4 variables.
  So 17 x 3 = 51 terms
  Three variables will again create 3 terms
  So 3x3 = 9 terms
  Adding 51 + 9 = 60 Answer
• 11 years agoHelpfull: Yes(0) No(3)
• answer is 1)49 as
  (1+x)^2=1+2x+x^2=3
  (1+x+x^2)^2=1+x^2+x^4+2x+2x^3+2x^2=1+3x^2+x^4+2x+2x^3=5
  so formula =mn+1(where m=total terms-1,n-power )
  so m=3,n=16
  solution=16*3+1=49
  
  
• 10 years agoHelpfull: Yes(0) No(0)