Bài làm:
Ta có: \(80^2-75^2+70^2-65^2+60^2-...+10^2-5^2\)
\(=\left(80-75\right)\left(80+75\right)+\left(70-65\right)\left(70+65\right)+...+\left(10-5\right)\left(10+5\right)\)
\(=5.\left(80+75\right)+5.\left(70+65\right)+...+5.\left(10+5\right)\)
\(=5.\left(80+75+70+65+...+10+5\right)\)
\(=5\cdot\frac{\left(5+80\right)\cdot\left[\left(80-5\right)\div5+1\right]}{2}\)
\(=5\cdot\frac{85\cdot16}{2}=3400\)