Question

(3a-2b)^3+(2b-5c)^3+(5c-3a)^3 factorize it

Answer 1

 (3a-2b)3+(2b-5c)3+(5c-3a)3 

Step by step solution :

Step  1  :

 1.1    Evaluate :  (5c-3a)3   =  125c3-225ac2+135a2c-27a3 

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   -54a2b + 135a2c + 36ab2 - 225ac2 - 60b2c + 150bc2  = 

  -3 • (18a2b - 45a2c - 12ab2 + 75ac2 + 20b2c - 50bc2) 

Trying to factor by pulling out :

 2.2      Factoring:  18a2b - 45a2c - 12ab2 + 75ac2 + 20b2c - 50bc2 

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

Group 1:  20b2c - 12ab2 
Group 2:  18a2b - 45a2c 
Group 3:  75ac2 - 50bc2 

Pull out from each group separately :

Group 1:   (3a - 5c) • (-4b2)
Group 2:   (2b - 5c) • (9a2)
Group 3:   (3a - 2b) • (25c2)

Looking for common sub-expressions : 

Group 1:   (3a - 5c) • (-4b2)
Group 3:   (3a - 2b) • (25c2)
Group 2:   (2b - 5c) • (9a2)

Answer 2

  (3a - 2b)^3 + (2b - c)^3 + (c - 3a)^3 
since 
(3a - 2b) + (2b - c) + (c - 3a) = 0 

therefore 
(3a - 2b)^3 + (2b - c)^3 + (c - 3a)^3 
= 3(3a - 2b)(2b - c)(c - 3a)Source(s):if a + b + c = 0 
then a + b = -c 
cubing both sides 
(a + b)^3 = -c^3 
a^3 + b^3 + 3a^2b + 3ab^2 = -c^3 
a^3 + b^3 = -c^3 -3ab(a+b) 
a^3 + b^3 + c^3 - = 3abc [because a+b = -c]