1. **Problem Statement:** Factor the expression $x^4 - 36$ using the difference of squares formula. 2. **Formula and Rules:** The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$. 3. **Step 1:** Recognize that $x^4 - 36$ can be written as $(x^2)^2 - 6^2$. 4. **Step 2:** Apply the difference of squares formula: $$x^4 - 36 = (x^2 - 6)(x^2 + 6)$$ 5. **Step 3:** Check if either factor can be factored further. $x^2 - 6$ and $x^2 + 6$ are not difference or sum of squares or cubes, so they cannot be factored further over the real numbers. 6. **Final Answer:** $$x^4 - 36 = (x^2 - 6)(x^2 + 6)$$ --- 1. **Problem Statement:** Factor the expression $k^3 - 27$ using the difference of cubes formula. 2. **Formula and Rules:** The difference of cubes formula is: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ 3. **Step 1:** Recognize that $k^3 - 27$ can be written as $k^3 - 3^3$. 4. **Step 2:** Apply the difference of cubes formula: $$k^3 - 27 = (k - 3)(k^2 + 3k + 9)$$ 5. **Step 3:** Check if the quadratic factor $k^2 + 3k + 9$ can be factored further. Since its discriminant $3^2 - 4 \times 1 \times 9 = 9 - 36 = -27$ is negative, it cannot be factored over the real numbers. 6. **Final Answer:** $$k^3 - 27 = (k - 3)(k^2 + 3k + 9)$$