Question

Factorize 1-3x-3y-4(x+y)^2

Answer 1

Answer :

(1 - 4x - 4y) (1 + x + y)

Step by step solution :

{ We factorize the given polynomial by middle term method. }

Now, 1 - 3x - 3y - 4 (x + y)²

= 1 - 3 (x + y) - 4 (x + y)²

= 1 - (4 - 1) (x + y) - 4 (x + y)²

= 1 - 4 (x + y) + 1 (x + y) - 4 (x + y)²

= {1 - 4 (x + y)} + (x + y) {1 - 4 (x + y)}

= {1 - 4 (x + y)} {1 + (x + y)}

= (1 - 4x - 4y) (1 + x + y) ,

which is the required factorization.

Another method :

Let us take x + y = p

Then, 1 - 3x - 3y - 4 (x + y)²

= 1 - 3 (x + y) - 4 (x + y)²

= 1 - 3p - 4p² , since x + y = p

= 1 + (1 - 4) p - 4p²

= 1 + p - 4p - 4p²

= 1 (1 + p) - 4p (1 + p)

= (1 + p) (1 - 4p)

= (1 + x + y) (1 - 4x - 4y) , since p = x + y

which is the required factorization.