Resolve each of the following quadratic trinomials into factors:6x2 -

1.	Resolve each of the following quadratic trinomials into factors:6x2 - 5xy - 6y2
Answer» 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)

Resolve each of the following quadratic trinomials into factors:6x2 - 5xy - 6y2

Answer»

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)