Resolve each of the following quadratic trinomials into factors:
Here, coefficient of x2 = 15, coefficient of x = -16yz and constant term = - 15y2z2
We shall now split up the coefficient of middle term i.e., -16yz into two parts whose sum is -16yz and product is 15 (-15y2z2) = - 225y2z2
Clearly,
-25yz + 9yz = -16yz and,
(-25yz) (9yz) = - 225y2z2
So, we replace middle term -16xyz = -25yz – 9yz
Thus, we have
15x2 -16xyz- 15y2z2 = 15x2 - 25yz + 9yz - 15y2z2
= 5x (3x – 5yz) + 3yz (3x – 5yz)
= (5x + 3yz) (3x - 5yz)