567 x 34 + 567 x 67 x 567 - 567
= 567 x 34 + 567 x 37989 - 567
= 567 x ( 34 + 37989 ) - 567
= 567 x 38023 - 567
= 21559041 - 567
= 2558474
\(567\times34+567\times67-567\)
\(=567\times34+567\times67-567\times1\)
\(=567\left(34+67-1\right)\)
\(=567\times100=56700\)