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)


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