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Resolve each of the following quadratic trinomials into factors:

6x2 - 5xy - 6y2

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Here, coefficient of x2 = 6, coefficient of x = -5y and constant term = - 6y2

We shall now split up the coefficient of middle term i.e., -5y into two parts whose sum is -5y and product is 6 (-6y2) = - 36y2

Clearly,

4y – 9y = -5y and

(4y) (-9y) = - 36y2

So, we replace middle term -5xy = 4xy – 9xy

Thus, we have

6x2 -5xy- 6y2 = 6x2 + 4xy - 9xy - 6y2

= (2x – 3y) (3x + 2y)

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