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)