\(34\cdot\left(-84\right)+17\cdot\left(-32\right)\)
\(=17\cdot2\cdot\left(-84\right)+17\cdot\left(-32\right)\)
\(=17\cdot\left(-168\right)+17\cdot\left(-32\right)\)
\(=17\cdot\left(-168-32\right)\)
\(=17 \cdot\left(-200\right)\)
\(= \left(-3400\right)\)