1. The problem is to expand and simplify the expression $ (x+1)(x+2)(x+3) $. 2. First, multiply the first two binomials: $ (x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2 $. 3. Now multiply this result by the third binomial: $ (x^2 + 3x + 2)(x+3) $. 4. Distribute each term in $ x^2 + 3x + 2 $ over $ x + 3 $: - $ x^2 \times x = x^3 $ - $ x^2 \times 3 = 3x^2 $ - $ 3x \times x = 3x^2 $ - $ 3x \times 3 = 9x $ - $ 2 \times x = 2x $ - $ 2 \times 3 = 6 $ 5. Combine all the terms: $ x^3 + 3x^2 + 3x^2 + 9x + 2x + 6 $. 6. Simplify like terms: $ x^3 + (3x^2 + 3x^2) + (9x + 2x) + 6 = x^3 + 6x^2 + 11x + 6 $. Final answer: $ x^3 + 6x^2 + 11x + 6 $.