Simplifying the Expression (x+3)(x^23x+9)(x2)(x^2+2x+4)
This expression involves the multiplication of two sets of binomials. The key to simplifying this expression lies in recognizing that both sets of binomials are in the form of (a+b)(a^2ab+b^2) and (ab)(a^2+ab+b^2) respectively, which are special cases of the difference of cubes formula.
Understanding the Difference of Cubes Formula:
The difference of cubes formula states: a³  b³ = (a  b)(a² + ab + b²)
Similarly, the sum of cubes formula is: a³ + b³ = (a + b)(a²  ab + b²)
Applying the Formula to our Expression:

Identify a and b:
 In the first set of binomials, a = x and b = 3.
 In the second set of binomials, a = x and b = 2.

Apply the difference of cubes formula:
 (x+3)(x^23x+9) = x³ + 3³ = x³ + 27
 (x2)(x^2+2x+4) = x³  2³ = x³  8

Substitute the simplified terms back into the original expression:
 (x+3)(x^23x+9)  (x2)(x^2+2x+4) = (x³ + 27)  (x³  8)

Simplify the expression:
 x³ + 27  x³ + 8 = 35
Therefore, the simplified expression (x+3)(x^23x+9)(x2)(x^2+2x+4) is equal to 35.