1. **State the problem:** Multiply the expressions $(-7x^2 + 9x - 15)$ and $(8x - 8)$. 2. **Formula and rules:** To multiply two polynomials, use the distributive property: multiply each term in the first polynomial by each term in the second polynomial, then combine like terms. 3. **Multiply each term:** $(-7x^2) \times 8x = -56x^3$ $(-7x^2) \times (-8) = +56x^2$ $(9x) \times 8x = 72x^2$ $(9x) \times (-8) = -72x$ $(-15) \times 8x = -120x$ $(-15) \times (-8) = +120$ 4. **Combine like terms:** $-56x^3 + (56x^2 + 72x^2) + (-72x - 120x) + 120$ $= -56x^3 + 128x^2 - 192x + 120$ 5. **Final answer:** $$-56x^3 + 128x^2 - 192x + 120$$