\(a.\)
\(34.\left(-84\right)+17.\left(-32\right)\)
\(=17.\left(-168\right)+17.\left(-32\right)\)
\(=17.\left(-168+-32\right)\)
\(=17.\left(-200\right)\)
\(=-3400\)
\(b.\)
\(4524+\left(-864\right)+9999+\left(-36\right)+\left(-8999\right)\)
\(=\left[4524+\left(-864\right)\right]+\left[9999+\left(-8999\right)\right]+\left(-36\right)\)
\(=3660+1000+\left(-36\right)\)
\(=4624\)
\(c.\)
\(1000+\left(-137\right)+263+\left(-572\right)+\left(-291\right)\)
\(=\left[263+\left(-572\right)+\left(-291\right)\right]+1000+\left(-137\right)\)
\(=\left(-600\right)+1000+\left(-137\right)\)
\(=400+\left(-137\right)\)
\(=263\)
\(d.\)
\(\left(-329\right)+15+\left(-101\right)+440+\left(-25\right)\)
\(=\left[15+\left(-25\right)\right]+\left[440+\left(-101\right)+\left(-329\right)\right]\)
\(=\left(-10\right)+10\)
\(=0\)
