1. The problem is to expand and simplify the expression $ (x + 2)(x + 3)(x + 6) $. 2. We start by multiplying the first two binomials: $ (x + 2)(x + 3) $. Using the distributive property (FOIL method), we get: $$ (x + 2)(x + 3) = x \cdot x + x \cdot 3 + 2 \cdot x + 2 \cdot 3 = x^2 + 3x + 2x + 6 = x^2 + 5x + 6 $$ 3. Now multiply the result $ x^2 + 5x + 6 $ by the third binomial $ (x + 6) $: $$ (x^2 + 5x + 6)(x + 6) = x^2 \cdot x + x^2 \cdot 6 + 5x \cdot x + 5x \cdot 6 + 6 \cdot x + 6 \cdot 6 $$ 4. Simplify each term: $$ = x^3 + 6x^2 + 5x^2 + 30x + 6x + 36 $$ 5. Combine like terms: $$ x^3 + (6x^2 + 5x^2) + (30x + 6x) + 36 = x^3 + 11x^2 + 36x + 36 $$ 6. The fully expanded and simplified expression is: $$ \boxed{x^3 + 11x^2 + 36x + 36} $$