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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