Rewrite the following to simplest factor form:  8+ (x-3)3

The expression 8 + (x-3)³ can't be simplified further as it is already in its simplest form. The cube of (x-3) can't be simplified without knowing the value of x.

The expression 8 + (x-3)³ is already in its simplest form. However, if you want to expand it, you can do so as follows:

1. Expand the cube (x-3)³ using the formula a³-b³ = (a-b)(a²+ab+b²). Here, a = x and b = 3.

   So, (x-3)³ = (x-3)[(x)² + (x)(3) + (3)²] = (x-3)(x² + 3x + 9)

2. Distribute (x-3) into each term inside the parenthesis:

   (x-3)(x² + 3x + 9) = x³ - 3x² + 3x² - 9x + 9x - 27 = x³ - 27

3. Now, add 8 to the expanded form of (x-3)³:

   8 + (x-3)³ = 8 + x³ - 27 = x³ - 19

So, the expression 8 + (x-3)³ simplifies to x³ - 19 when expanded.