Question

因式分解,11的三次方+12的三次方+13的三次方+14的三次方+15的三次方

Answer 1

11^3+12^3+13^3+14^3+15^3

=(1^3+2^3+……+15^3)-(1^3+2^3+……+10^3)

=(1+2+3+……+15)^2-(1+2+……+10)^2

=[(1+15)*15/2]^2-[(1+10)*10/2]^2

=120^2-55^2

=(120+55)(120-55)

=175*65

=11375