99th row of pascal's triangle:
1 , 9 , 36 , 84 , 126 , 126 , 84 , 36 , 9 , 1
the powers of each term in the binomial expression always add to 9:9:
(x^9)(-2^0)+(x^8)(-2^1)+(x^7)(-2^2)+(x^6)(-2^3)+(x^5)(-2^4)+(x^4)(-2^5)+(x^3)(-2^6)+(x^2)(-2^7)+(x^1)(-2^8)+(x^0)(-2^9)(x9)(−20)+(x8)(−21)+(x7)(−22)+(x6)(−23)+(x5)(−24)+(x4)(−25)+(x3)(−26)+(x2)(−27)+(x1)(−28)+(x0)(−29)
when each term is multiplied by its corresponding coefficient, this becomes
1(x^9)(-2^0)+ 9(x^8)(-2^1)+ 36(x^7)(-2^2)+ 84(x^6)(-2^3)+ 126(x^5)(-2^4)+ 126(x^4)(-2^5)+ 84(x^3)(-2^6)+ 36(x^2)(-2^7)+ 9(x^1)(-2^8)+1(x^0)(-2^9)
n^0=1
(x^9)+ 9(x^8)((-2)^1)+ 36(x^7)((-2)^2)+ 84(x^6)((-2)^3)+ 126(x^5)((-2)^4)+ 126(x^4)((-2)^5)+ 84(x^3)((-2)^6)+ 36(x^2)((-2)^7)+ 9(x^1)((-2)^8)+((-2)^9)
=x^9+ 9x^8(-2)^1+ 36(x^7)((-2)^2)+ 84(x^6)((-2)^3)+ 126(x^5)((-2)^4)+ 126(x^4)(-2)^5+ 84(x^3)((-2)^6)+ 36(x^2)((-2)^7)+ 9(x^1)((-2)^8)+((-2)^9)
=x^9 -18x^8 + 144x^7 -672x^6 + 2016x^5 -4032x^4 +5376x^3 -4608^2 + 2304x -512
=x^9 -18x^8 + 144x^7 -672x^6 + 2016x^5 -4032x^4 +5376x^3 -4608^2 + 2304x -512
