Algebraic Pattern Math Example 2

Solution

1. 1
   Step 1: Recognize: $x^3 - 27 = x^3 - 3^3$ (difference of cubes).
2. 2
   Step 2: Apply $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ with $a = x, b = 3$.
3. 3
   Step 3: $(x - 3)(x^2 + 3x + 9)$.
4. 4
   Check: $(x-3)(x^2+3x+9)$ at $x = 3$: $0 \times 27 = 0$ and $27 - 27 = 0$ ✓