What is the digit in the units place of the number \(48 \times (234)^{100} + (234)^{101}\)?

The units digit is 2. Take out the common factor: $48 \times 234^{100} + 234^{101}$ $= 234^{100}(48 + 234)$ $= 234^{100} \times 282$. Powers of 4 end in 4 (odd power) or 6 (even power), so $234^{100}$ ends in 6. Then 6 × 2 = 12, which ends in 2. Reading 6 as the final digit forgets the factor 282.