Question

(a^2+b^2)(c-d)(a-2b)

Answer 1

Step 1 :

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

1.2     Evaluate :  (c-d)2   =    c2-2cd+d2

Trying to factor by pulling out :

1.3      Factoring:  a2-2ab+b2-c2+2cd-d2

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

Group 1:  2cd-c2

Group 2:  -2ab+a2

Group 3:  b2-d2

Pull out from each group separately :

Group 1:   (c-2d) • (-c)

Group 2:   (a-2b) • (a)

Group 3:   (b2-d2) • (1)

Looking for common sub-expressions :

Group 1:   (c-2d) • (-c)

Group 3:   (b2-d2) • (1)

Group 2:   (a-2b) • (a)

Bad news !! Factoring by pulling out fails :

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

Final result :

 a2 - 2ab + b2 - c2 + 2cd - d2