Simplify the following:
12 y^2+9 y^2+17 y-13 y-4+3
Grouping like terms, 12 y^2+9 y^2+17 y-13 y-4+3 = (12 y^2+9 y^2)+(17 y-13 y)+(-4+3):
(12 y^2+9 y^2)+(17 y-13 y)+(-4+3)
12 y^2+9 y^2 = 21 y^2:
21 y^2+(17 y-13 y)+(-4+3)
17 y-13 y = 4 y:
21 y^2+4 y+(-4+3)
3-4 = -1:
21 y^2+4 y+-1
Factor the quadratic 21 y^2+4 y-1. The coefficient of y^2 is 21 and the constant term is -1. The product of 21 and -1 is -21. The factors of -21 which sum to 4 are -3 and 7. So 21 y^2+4 y-1 = 21 y^2+7 y-3 y-1 = (7 y-1)+3 y (7 y-1):
(7 y-1)+3 y (7 y-1)
Factor 7 y-1 from (7 y-1)+3 y (7 y-1):
Answer: | (7y-1) (3y+1)
