a) 

\(P=\left(x^{14}-9x^{13}\right)-\left(x^{13}-9x^{12}\right)+\left(x^{12}-9x^{11}\right)-...+\left(x^2-9x\right)-\left(x-9\right)+1\)

\(=x^{13}\left(x-9\right)-x^{12}\left(x-9\right)+x^{11}\left(x-9\right)+...+x\left(x-9\right)-\left(x-9\right)+1\)

\(P\left(9\right)=1\)

b)

\(Q=\left(x^{15}-7x^{14}\right)-\left(x^{14}-7x^{13}\right)+\left(x^{13}-7x^{12}\right)-...-\left(x^2-7x\right)+\left(x-7\right)+2\)

\(=x^{14}\left(x-7\right)-x^{13}\left(x-7\right)+x^{12}\left(x-7\right)-...-x\left(x-7\right)+\left(x-7\right)+2\)

\(Q\left(7\right)=2\)

a, \(A=x^3-30x^2-31x+1\)

\(=x^3-31x^2+x^2-31x+1\)

\(=x^2\left(x-31\right)+x\left(x-31\right)+1\)

\(=\left(x^2+x\right)\left(x-31\right)+1\)

Thay x = 31 \(\Rightarrow A=1\)

Vậy A = 1 khi x = 31

b, tách ra làm tương tự phần a

C = x¹⁴ - 10x¹³ + 10x¹³ -10x¹¹ + ... + 10x¹² -10x + 10 

    = x¹⁴ - ( x + 1 )x¹³ + ( x + 1)x¹² -... - ( x + 1)x + 10 + 1

    =x¹⁴ -x¹⁴ - x¹³ + x¹³ + x¹² - ...- x² - x + 10 + 1 

     = 1

Không chắc lắm

phan h 10=9+1

 x=9=>10=x+1

thqy 10=x+1 vào A

ta có A=x^14 - (x+1)x^13+(x+1)x^12-(x+1)x^11+...+(x+1)x^2-(x+1)x+10

          =x^14-x^14-x^13+x^13+x^12-x^12-x^11+...+x^3+x^2-x^2_x+10

          =x+10

          mà x=9 

         =>A=19

dễ ợt . tui làm chắc chắn đúng nè 
ta có : x=9 suy ra 10=x+1. do đó 
C= (x+1)x^14 - (x+1)x^13 + (x+1)x^12 - (x+1)x^11 + ..... + (x+1)x^2 - (x+1)x + 10 
= x^15 + x^14 - x^14 - x^13 + x^13 + x^12 - x^12 - x^11 + ... + x^3 + x^2 - x^2 - x +10 
=x^15 -x +10 = 9^15 - 9 +10 = 
C=9^15 +1

Ta có 10=9+1=x+1(Vì x=9)

=>B= x¹⁴-(x+1)x¹³+(x+1)x¹²-(x+1)x¹¹+.........-(x+1)x+10

=>B= x¹⁴-x¹⁴-x¹³+x¹³+x¹²-x¹²-x¹¹+.....-x²-x+10

=>B=-x+10

Thay x=9, ta có

B=-9+10=1

\(B=x^{14}-10x^{13}+10x^{12}-10x^{11}+...+10x^2-10x+10\)

\(=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-\left(x+1\right)x^{11}+...+\left(x+1\right)x^2-\left(x+1\right)x+x+1\)

\(=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-x^{12}-x^{11}+...+x^3+x^2-x^2-x+x+1\)

\(=1\)

a)    Ta có : \(x=31\Rightarrow30=x-1\)

Thay vào biểu thức ta được:

\(A=x^3-\left(x-1\right).x^2-x^2+1=x^3-x^3+x^2-x^2+1=1\)

b) Ta có: \(x=9\Rightarrow x+1=10\)

Thay vào biểu thức ta được

\(B=x^{14}-\left(x+1\right).x^{13}+\left(x+1\right).x^{12}-\left(x+1\right).x^{11}+.....+x^2.\left(x+1\right)=\left(x+1\right).x+\left(x+1\right)\)

\(\Leftrightarrow B=x^{14}-x^{14}-x^{13}+x^{13}+....+x^3+x^2=x^2+2x+1\)

\(\Leftrightarrow B=x^2-x^2-2x-1=-2.9-1=-19\)

\(x^{14}-10x^{13}+10x^{12}-10x^{11}+...+10x^2-10x+10\)

\(=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-\left(x+1\right)x^{11}+..+\left(x+1\right)x^2-\left(x+1\right)x+x+1\)

\(=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-x^{12}-x^{11}+...+x^3+x^2-x^2-x+x+1\)

\(=1\)

`5x(4x^2-2x+1)-2x(10x^2-5x-2)`

`= 20x^3-10x^2+5x - (20x^3-10x^2-4x)`

`=9x`

Thay `x=15` có: `9.15=135`.

Mk k ghi lại đề mà lm lun nha!

= 9¹⁴ - (9+1)9¹³ + (9+1)9¹² - (9+1)9¹¹ +...+ (9+1)9² - (9+1)9 + 10

= 9¹⁴ - 9¹⁴  - 9¹³  + 9¹³ + 9¹² - 9¹² - 9¹¹ +...+ 9³ + 9² -9² + 9 +10

= 9 + 10 = 19

Bài mk giải k pk kết quả đúng or sai, có j sửa giùm mk lun nha

Bằng 19 nhà bạn anh mình lấy. Nick mình

Với \(x=9\)\(\Rightarrow x+1=10\)

\(\Rightarrow x^{14}-10x^{13}+10x^{12}-10x^{11}+......+10x^2-10x+10\)

\(=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-.......-\left(x+1\right).x+\left(x+1\right)\)

\(=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-........-x^2-x+x+1=1\)

x=9

=>x+1=10

\(A=x^{10}-10x^9+10x^8-...+10x^2-10x+1\)

\(=x^{10}-x^9\left(x+1\right)+x^8\left(x+1\right)-...+x^2\left(x+1\right)-x\left(x+1\right)+1\)

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

=-x+1

=-9+1=-8