Question

Bài 1: Rút gọn biểu thức

a) a(a-b) + b(a-b)

b) a^n-1(a+b) - b(a^n-1+b^n-1)

Answer 1

\(a,a\left(a-b\right)+b\left(a-b\right)\)

\(=\left(a-b\right)\left(a+b\right)\)

\(=a^2-b^2\)

\(b,a^{n-1}\left(a+b\right)-b\left(a^{n-1}+b^{n-1}\right)\)

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

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

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

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

Answer 2

\(a,\)\(a\left(a+b\right)+b\left(a-b\right)\)

\(=\left(a+b\right)\left(a-b\right)\)

\(=a^2-b^2\)

\(b,\) \(a^{n+1}\left(a+b\right)-b\left(a^{n+1}+b^{n-1}\right)\)

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

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