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denis23 [38]
3 years ago
6

How do i do 3 part a ?

Mathematics
1 answer:
WINSTONCH [101]3 years ago
6 0


In general the binomial expansion is


(a+b)^n = {n \choose 0} a^0 b^n + {n \choose 1} a^1 b^{n-1} + {n \choose 2} a^2 b^{n-2} + ... + {n \choose n} a^n b^0


So in our case, because we want ascending powers of x we'll write,


(-3x + 1)^{11} =  {11 \choose 0} (-3x)^0 1^{11} + {11 \choose 1} (-3x)^{1} 1^{10} + {11 \choose 2} (-3x)^{2} 1^9  + {11 \choose 3 } (-3x)^3 1^8 + ...


We need to calculate the binomial coefficients:


{11 \choose 0}  = 1


{11 \choose 1}  = 11


{11 \choose 2}  = \dfrac{11 \times 10}{2} = 55


{11 \choose 3}  = \dfrac{11 \times 10 \times 9}{3 \times 2} = 165


(-3x+1)^{11} =  1 (-3x)^0 1^{11}  + 11(-3x)^{1} 1^{10}  + 55 (-3x)^2 1^{9}  + 165 (-3x)^3 1^8 + ...


(1-3x)^{11} =  1 -33 x + 495 3x^2 - 4455 x^3+ ...



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