Question

Can anyone answer this question of factorisation : -

1 - 2a - 2b - 3(a + b)^2​

Answer 1

3a2 - 6ab - 2a - 3b2 - 2b + 1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(-2a - 2b + 1) - 3 • (a + b)2

Step  2  :

 2.1    Evaluate :  (a+b)2   =  a2+2ab+b2 

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -3a2 - 6ab - 2a - 3b2 - 2b + 1  = 

  -1 • (3a2 + 6ab + 2a + 3b2 + 2b - 1) 

Trying to factor by pulling out :

 3.2      Factoring:  3a2 + 6ab + 2a + 3b2 + 2b - 1 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  2b + 2a 

Group 2:  6ab + 3a2 

Group 3:  3b2 - 1 

Pull out from each group separately :

Group 1:   (a + b) • (2)

Group 2:   (a + 2b) • (3a)

Group 3:   (3b2 - 1) • (1)

Looking for common sub-expressions :

Group 1:   (a + b) • (2)

Group 3:   (3b2 - 1) • (1)

Group 2:   (a + 2b) • (3a

The groups have no common factor and can not be added up to form a multiplication.

Final result :

-3a2 - 6ab - 2a - 3b2 - 2b +

Hope that helps u mate ♡♡♡♡♡