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

1.	Resolve each of the following quadratic trinomials into factors:6x2 – 13xy + 2y2
Answer» 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)

Resolve each of the following quadratic trinomials into factors:6x2 – 13xy + 2y2

Answer»

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)