Q. 183.6( 7 Votes )

Resolve each of the following quadratic trinomials into factors:


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)


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