1. **State the problem:** Simplify the expression $6x^2 - 54$. 2. **Identify the formula or rule:** We can factor out the greatest common factor (GCF) from the terms. 3. **Find the GCF:** The GCF of $6x^2$ and $54$ is $6$. 4. **Factor out the GCF:** $$6x^2 - 54 = 6(x^2 - 9)$$ 5. **Recognize the difference of squares:** $x^2 - 9$ is a difference of squares since $9 = 3^2$. 6. **Apply the difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ So, $$x^2 - 9 = (x - 3)(x + 3)$$ 7. **Write the fully factored form:** $$6x^2 - 54 = 6(x - 3)(x + 3)$$ **Final answer:** $6(x - 3)(x + 3)$