Use the binomial theorem to find the seventh term in the exp

Use the binomial theorem to find the seventh term in the expansion of (x -2)^9. The seventh term is (Simplify your answer)

Solution

Binomial theorem is

(x+y)^n= nC0 x^ny^0 + nC1 x^(n-1)y^1 + nC2 x^(n-2)y^2 + nC3 x^(n-4)y^4+........+ nCn x^0 y^n

(x-2)^9= 9C0 x^9 (-2)^0 +9C1 x^8 (-2)^1+ 9C2 x^7 (-2)^2 + 9C3 x^6(-2)^3 + 9C4 x^5 (-2)^4 + 9C5 x^4 (-2)^5 + 9C6       x^3(-2)^6 + 9C7 x^2(-2)^7 + 9C8 x^1(-2)^8 + 9C9 x^0(-2)^9

seventh term is 9C6 x^3(-2)^6= 5376x^3