Exploring the Expression: (x+2)^3 + (x2)^3  2x(x^2 + 12)
This article will explore the algebraic expression (x+2)^3 + (x2)^3  2x(x^2 + 12). We will simplify the expression and discuss its properties.
Simplifying the Expression
We can simplify the expression using the following steps:

Expand the cubes:
 (x+2)^3 = (x+2)(x+2)(x+2) = x^3 + 6x^2 + 12x + 8
 (x2)^3 = (x2)(x2)(x2) = x^3  6x^2 + 12x  8

Substitute the expanded expressions: (x^3 + 6x^2 + 12x + 8) + (x^3  6x^2 + 12x  8)  2x(x^2 + 12)

Simplify: 2x^3 + 24x  2x^3  24x = 0
Therefore, the simplified form of the expression is 0.
Conclusion
The expression (x+2)^3 + (x2)^3  2x(x^2 + 12) simplifies to 0. This means that the expression is equal to zero regardless of the value of x. This is a constant expression, and its value will always be zero.
This analysis demonstrates how algebraic manipulations can be used to simplify complex expressions and reveal hidden relationships.