Question

Simplify 2x+x+x+2yX3yXy

Answer 1

Answer:

2x • (x^3y^3 + 2)

Step-by-step explanation:

4x +  (2x3y • y) • x) • y)

Pulling out like terms :

3.1     Pull out like factors :

  2x4y3 + 4x  =   2x • (x3y3 + 2)

Trying to factor as a Sum of Cubes :

3.2      Factoring:  x3y3 + 2

Theory : A sum of two perfect cubes,  a3 + b3 can 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 :  2  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cube

Final result :

 2x • (x^3y^3 + 2)

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