Resolve each of the following quadratic trinomials into factors:
6x2 – 13xy + 2y2
Here, coefficient of x2 = 6, coefficient of x = -13y and constant term = 2y2
We shall now split up the coefficient of middle term i.e., -13y into two parts whose sum is -13y and product is 6 (2y2) = 12y2
Clearly,
-12y – y = -13y and,
(-12y) (-y) = 12y2
So, we replace middle term -13xy = -12xy – xy
Thus, we have
6x2 -13xy+ 2y2 = 6x2 - 12xy - xy - 2y2
= (6x – y) (x - 2y)