f(100)=x⁸-(100+1)x⁷+(100+1)x⁶-(100+1)x⁵+....+(100+1)x²-(100+1)x+25

=x⁸-(x+1)x⁷+(x+1)x⁶-(x+1)x⁵+....+(x+1)x²-(x+1)x+25

=x⁸-x⁸-x⁷+x⁷+x⁶-x⁶-x⁵+...+x³+x²-x²-x+25

=25

vậy f(100)=25

Mk ko hiểu lắm! Hoàng Phúc

-x+25=25?

Ta có: 101 = 100+1=x+1

Khi đó :

\(f\left(x\right)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25\)

\(f\left(x\right)=x^8-\left(x+1\right)x^7+\left(x+1\right)x^6-\left(x+1\right)x^5+.....+\left(x+1\right)x^2-\left(x+1\right)x+25\)

\(f\left(x\right)=x^8-x^8-x^7+x^7+x^6-x^6+x^5+...+x^3+x^2-x^2-x+25\)

\(f\left(x\right)=-x+25\)

Vậy \(f\left(100\right)=-100+25=-75\)

f(100)=> x=100

=>x+1=101

thay x+1=101 ta được:

f(100)=x⁸-(x+1)x⁷+(x+1)x⁶-(x+1)x⁵+...+(x+1)x²-(x+1)x+25

=x⁸-(x⁸+x⁷)+(x⁷+x⁶)-(x⁶+x⁵)+...+(x³+x²)-(x²+x)+25

=x⁸-x⁸-x⁷+x⁷+x⁶-x⁶-x⁵+...+x³+x²-x²-x+25

=-x+25

=-100+25

=-75

-75 nha

Trả lời siêu quá

\(x=100\Rightarrow x+1=101\)

\(f\left(x\right)=x^8-\left(x+1\right).x^7+\left(x+1\right).x^6-\left(x+1\right).x^5+....+\left(x+1\right).x^2+\left(x+1\right).x+25\)

\(f\left(x\right)=x^8-x^8-x^7+x^7+x^6-x^6-x^5+.....+x^3+x^2-x^2+x+25\)

\(f\left(100\right)=100+25=125\)

F(x)=x⁸-100x⁷-x⁷+100x⁶+x⁶-100x⁵-x⁵+......+100x²+x²-100x-x+25

f(x)=x⁷(x-100)-x⁶(x-100)+x⁵(x-100)-......+x(x-100)-(x-25)

f(100)=100⁷.(100-100)-100⁶(100-100)+......+100(100-100)-(100-25)

f(100)=-75

Vậy f(100)=-75