Resolve each of the following quadratic trinomials into factors:14x2 +

1.	Resolve each of the following quadratic trinomials into factors:14x2 + 11xy - 15y2
Answer» Here, coefficient of x² = 14, coefficient of x = 11y and constant term = - 15y² We shall now split up the coefficient of middle term i.e., 11y into two parts whose sum is 11y and product is 14 (-15y²) = - 210y² Clearly, 21y – 10y = 11y and (21y) (-10y) = - 210y² So, we replace middle term 11xy = 21xy – 10xy Thus, we have 14x² + 11xy- 15y² = 14x² + 21xy - 10xy - 15y² = 2x (7x – 5y) + 3y (7x – 5y) = (2x + 3y) (7x - 5y)

Resolve each of the following quadratic trinomials into factors:14x2 + 11xy - 15y2

Answer»

Here, coefficient of x² = 14, coefficient of x = 11y and constant term = - 15y²

We shall now split up the coefficient of middle term i.e., 11y into two parts whose sum is 11y and product is 14 (-15y²) = - 210y²

Clearly,

21y – 10y = 11y and

(21y) (-10y) = - 210y²

So, we replace middle term 11xy = 21xy – 10xy

Thus, we have

14x² + 11xy- 15y² = 14x² + 21xy - 10xy - 15y²

= 2x (7x – 5y) + 3y (7x – 5y)

= (2x + 3y) (7x - 5y)