Resolve each of the following quadratic trinomials into factors:(x - 2

1.	Resolve each of the following quadratic trinomials into factors:(x - 2y)2 - 5(x - 2y) + 6
Answer» x² + 4y² – 4xy – 5x + 10y + 6 Here, coefficient of (x – 2y)² = 1, coefficient of (x – 2y ) = - 5 and constant = 6 We shall now split up the coefficient of middle term i.e., - 5 into two parts whose sum is -5 and product is 6 (1) = 6 Clearly, - 2 - 3 = - 5 and - 2 (-3) = 6 So, we replace - 5 (x – 3y) = - 2 (x – 2y) – 3 (x – 2y) Thus, we have (x – 2y)² – 5 (x – 2y) + 6 = (x – 2y)² – 2 (x – 2y) – 3 (x – 2y) + 6 = (x – 2y - 2) (x - 2y - 3)

Resolve each of the following quadratic trinomials into factors:(x - 2y)2 - 5(x - 2y) + 6

Answer»

x² + 4y² – 4xy – 5x + 10y + 6

Here, coefficient of (x – 2y)² = 1, coefficient of (x – 2y ) = - 5 and constant = 6

We shall now split up the coefficient of middle term i.e., - 5 into two parts whose sum is -5 and product is 6 (1) = 6

Clearly,

- 2 - 3 = - 5 and

- 2 (-3) = 6

So, we replace - 5 (x – 3y) = - 2 (x – 2y) – 3 (x – 2y)

Thus, we have

(x – 2y)² – 5 (x – 2y) + 6 = (x – 2y)² – 2 (x – 2y) – 3 (x – 2y) + 6

= (x – 2y - 2) (x - 2y - 3)