Factorise:
14pq + 35pqr

We have            14pq = 2 × 7 × p × q = 2 × (7 × p × q)

                         35pqr = 5 × 7 × p × q × r = 5 × (7 × p × q) × r

∴          14pq + 35 pqr = 2 × (7 × p × q) + 5 × (7 × p × q) × r

                                   = (7 × p × q)[2 + 5 × r]

                                   = 7pq(2+5r)














 

∵                                       12x = 2 × 2 × 3 × x = (2 × 2 × 3) × x

and                                    36 = 2 × 2 × 3 × 3 = (2 × 2 × 3) × 3

∴          the common factor = 2 × 2 × 3

                                          = 12

∵                  2y = 2 × y = (2 × y)

and             22xy = 2 × 11x × y = (2 × y) × 11x

∴   the common factor = 2 × y

                                   = 2y

We have                   22y = 2 × 11 × y

                                33z = 3 × 11 × z

∴                     22y - 33z = [2 × (11) × y] + [3 × (11) × z]
                                      
                                      = (11)[2 × y - 3 × z]

                                      = 11[2y - 3z]

We have    12x =

                   36 =

∴        12x + 36 = [(223)x] + (223) 3

                         =