Bài 5:
Ta có: x=100
nên x+1=101
Ta có: \(f\left(x\right)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25\)
\(=x^8-x^7\left(x+1\right)+x^6\left(x+1\right)-x^5\left(x+1\right)+...+x^2\left(x+1\right)-x\left(x+1\right)+25\)
\(=x^8-x^8-x^7+x^7+x^6-x^6-x^5+...+x^3+x^2-x^2-x+25\)
=-x+25
=-100+25
=-75
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Bài 5:
Ta có: x=100
nên x+1=101
Ta có: f(x)=x8−101x7+101x6−101x5+...+101x2−101x+25
=x8−x7(x+1)+x6(x+1)−x5(x+1)+...+x2(x+1)−x(x+1)+25
=x8−x8−x7+x7+x6−x6−x5+...+x3+x2−x2−x+25
=-x+25
=-100+25
=-75
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