To add the expressions \( a + b + ab \), \( b - c + bc \), and \( c + a + ac \), you can follow these steps:

1. Combine like terms for each expression.
2. Add the resulting expressions together.

Here's the arithmetic solution:

1. \( a + b + ab \)
2. \( b - c + bc \)
3. \( c + a + ac \)

Now, let's combine like terms:

1. \( a + b + ab \)
2. \( b - c + bc \)
3. \( c + a + ac \)

Now, add the expressions together:

\[ (a + b + ab) + (b - c + bc) + (c + a + ac) \]

Expanding, we get:

\[ a + b + ab + b - c + bc + c + a + ac \]

Now, combine like terms:

\[ a + a + b + b + b + c + c + ac + ab + bc \]

Now, simplify:

\[ 2a + 3b + 2c + ab + ac + bc \]

So, the sum of the expressions \( a + b + ab \), \( b - c + bc \), and \( c + a + ac \) is:

\[ 2a + 3b + 2c + ab + ac + bc \]

Solution:
The volume V of a cuboid is given by the formula:
V = Length × Width × Height

Given dimensions:
Length = (x² - 2)
Width = (2x + 4)
Height = (x - 3)

So, substituting these values into the formula, we get:
V = (x² - 2) × (2x + 4) × (x - 3)

Expanding the expression:
V = (x² - 2) × (2x + 4) × (x - 3)
V = (2x³ - 4x + 4x + 8) × (x - 3)
V = (2x³ + 8) × (x - 3)
V = 2x⁴ - 6x³ + 8x - 24

So, the volume of the cuboid is 2x⁴ - 6x³ + 8x - 24.

Solution:
To simplify the expression, we can use the distributive property:
(a + b + c)(a + b - c) = a(a + b - c) + b(a + b - c) + c(a + b - c)

Expanding each term:
= a² + ab - ac + ab + b² - bc + ac + bc - c²

Simplifying the terms:
= a² + 2ab - c²

So, the simplified expression is a² + 2ab - c².