Simplifying the Expression (x+2)^3  x(x+3)(x3)  12x^2  8
This article will guide you through simplifying the expression (x+2)^3  x(x+3)(x3)  12x^2  8. We'll break down each step and explain the reasoning behind it.
Expanding the Expression
Let's start by expanding the expression step by step:

(x+2)^3: This is a cube of a binomial. We can use the binomial theorem or simply multiply (x+2) by itself three times: (x+2)^3 = (x+2)(x+2)(x+2) = (x^2 + 4x + 4)(x+2) = x^3 + 6x^2 + 12x + 8

x(x+3)(x3): This is a product of three binomials. Notice that (x+3) and (x3) form a difference of squares pattern: x(x+3)(x3) = x(x^2  9) = x^3  9x

12x^2  8: This part remains unchanged for now.
Now, let's put everything together: (x+2)^3  x(x+3)(x3)  12x^2  8 = (x^3 + 6x^2 + 12x + 8)  (x^3  9x)  12x^2  8
Combining Like Terms
Finally, we can combine the like terms:
x^3 + 6x^2 + 12x + 8  x^3 + 9x  12x^2  8 = 6x^2 + 21x
Conclusion
Therefore, the simplified form of the expression (x+2)^3  x(x+3)(x3)  12x^2  8 is 6x^2 + 21x.