Question

Factorise the following:
12(2x - 3y)² - 2x + 3y - 1

Answer 1

12(2x - 3y)² - 1(2x - 3y) - 1
= 12a² - a - 1 [Taking (2x - 3y) = a]
= 12a² - 4a + 3a - 1
= 4a(3a - 1) + 1(3a - 1)
= (3a - 1)(4a + 1)
= [3(2x - 3y) - 1][4(2x - 3y) + 1]
= (6x - 9y - 1)(8x - 12y + 1).