(Come find me and I will help you!)

Problem 1 posted on 3/18/12

Factor (a+b)(a+2b)(a+3b)(a+4b) + 4b⁴

Problem 2 posted on 4/22/13

Factor a³ + b³ + c³ - 3abc 

Problem 3 posted on 12/24/13

It takes Bubaba 8 hours, Pupepe 3.6 hours, and Lulala 2 hours to build a gadget. At 1pm, Bruce Wayne called to request this gadget by 3 pm. Bubaba started right away. At 1:30, Pupepe joined Bubaba. What time should Lulala join them so that they can finish building the gadget at exactly 3pm?

There is only one positive integer which is exactly twice the sum of its digits. What is this two-digit number?