Question

The coefficient of x^7in the polynomial expansion of
(1 + 2x - x^2)^4 is​

Answer 1

Answer:

Step-by-step explanation: by multinomial

concept

we have general term in multinomial theorem as

n factorial/r factorial s factorial t factorial multiplied by a^r*b^s*c^t a

and condition is n =r+s+t

let substitute values that we have

n=4,a=1,b=2x and c= -x^2

4 factorial/r factorial s factorial t factorial (1)^r*(2x)^s*(-x^2)^t

4 factorial/ r factorial s factorial t factorial multiplied 2^s*(-1)t*x^2t+s

with above equation for getting x^7

2t+s=7

write possibilities

possibilities are

t=0 s=7 (this is wrong  because n=r+s+t here n is 4, means s value is less than equal to that

t=1  s=5(not possible beacuse of first condition)

t=2 s=3( not possible because of first postulate)

t=3 s=1 ( possible because of first postulate)

mean there is only one possibility that is t=3 s=1

and on more thing n=r+s+t

4=r+1+3

means r=0

substitute it in equation that we discussed

4 factorial/0 factorial*1 factorial*3 factorial multiplied x^7

coefficient=excluding x^7 in above equation=4 factorial / 3 factorial=4c1 or 4c3=4

@alakh pandey(physics ...ah