Question

Tính:

a, (x-1) . ( \(x^{n-1}+x^{n-2}+...+x^2+x+1\))

b, (a-b) . ( \(a^{n-1}+a^{n-2}.b+...+ab^{n-2}+b^{n-1}\))

c, (a+b) . ( \(a^{n-1}-a^{n-2}.b+a^{n-3}.b^2+...-b^{n-1}\))

Answer 1

a: \(\left(x-1\right)\left(x^{n-1}+x^{n-2}+...+x^2+x+1\right)\)

\(=x^n+x^{n-1}+...+x^3+x^2+x-x^{n-1}-x^{n-2}-...-x^2-x-1\)

\(=x^n-1\)

b: \(\left(a-b\right)\left(a^{n-1}+a^{n-2}b+...+ab^{n-2}+b^{n-1}\right)\)

\(=a^n+a^{n-1}b+...+a^2b^{n-2}+ab^{n-1}-a^{n-1}b-a^{n-2}b^2-...-ab^{n-1}-b^n\)

\(=a^n-b^n\)