a) \(-524\cdot\left[23+\left(-45\right)\right]+524\cdot\left(-45+123\right)\)
\(=-524\cdot\left[\left(23-45\right)-\left(-45+123\right)\right]\)
\(=-524\cdot\left(23-45+45-123\right)\)
\(=-524\cdot-100\)
\(=52400\)
b) \(47\cdot69-31\cdot\left(-47\right)\)
\(=-47\cdot\left(-69-31\right)\)
\(=-47\cdot-100\)
\(=4700\)
c) \(16\left(38-2\right)-38\left(16-1\right)\)
\(=16\cdot38-16\cdot2-38\cdot16+38\)
\(=-16\cdot2+38\)
\(=-36+38\)
\(=2\)
d) \(\left(-41\right)\cdot\left(59+2\right)+59\cdot\left(41-2\right)\)
\(=-41\cdot59-41\cdot2+41\cdot59-2\cdot59\)
\(=-41\cdot2-2\cdot59\)
\(=-2\left(41+59\right)\)
\(=-2\cdot100\)
\(=-200\)
e) \(25\cdot\left(-8\right)\cdot\left(-25\right)\cdot9\cdot4\cdot100^0:3\)
\(=\left(-1000\right)\cdot\left(-25\right)\cdot9\cdot4\cdot1:3\)
\(=25000\cdot9\cdot4:3\)
\(=25000\cdot3\cdot4\)
\(=100000\cdot3\)
\(=300000\)
