1. **State the problem:** Simplify or expand the expression $$(x-8)^3 (x+8)^4$$. 2. **Recall the binomial expansion formula:** $$(a+b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$$ 3. **Important note:** Expanding fully will be lengthy. Instead, recognize the structure and use properties of exponents and binomials. 4. **Rewrite the expression:** $$(x-8)^3 (x+8)^4 = (x-8)^3 (x+8)^3 (x+8) = ((x-8)(x+8))^3 (x+8)$$ 5. **Simplify the product inside the cube:** $$(x-8)(x+8) = x^2 - 64$$ 6. **Substitute back:** $$((x-8)(x+8))^3 (x+8) = (x^2 - 64)^3 (x+8)$$ 7. **Final simplified form:** $$ (x^2 - 64)^3 (x+8) $$ This is a simpler form than full expansion and often preferred for clarity and further use.