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)