Question

2acube +16b cube -5a-10b

Answer 1

2a3+16b3 

Final result :

2 • (a + 2b) • (a2 - 2ab + 4b2)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(2 • (a3)) + 24b3

Step  2  :

Equation at the end of step  2  :

2a3 + 24b3

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2a3 + 16b3  =   2 • (a3 + 8b3) 

Trying to factor as a Sum of Cubes :

 4.2      Factoring:  a3 + 8b3 

Theory : A sum of two perfect cubes,  a3 + b3can be factored into  :
             (a+b) • (a2-ab+b2)
Proof  : (a+b) • (a2-ab+b2) = 
    a3-a2b+ab2+ba2-b2a+b3 =
    a3+(a2b-ba2)+(ab2-b2a)+b3=
    a3+0+0+b3=
    a3+b3

Check :  8  is the cube of   2 
Check :  a3 is the cube of   a1

Check :  b3 is the cube of   b1

Factorization is :
             (a + 2b)  •  (a2 - 2ab + 4b2)