1. **State the problem:** Expand the expression $(-1 + 2p)(3 - 4p)$ and write the result as a polynomial in standard form. 2. **Recall the distributive property (FOIL method):** $$(a + b)(c + d) = ac + ad + bc + bd$$ where $a = -1$, $b = 2p$, $c = 3$, and $d = -4p$. 3. **Apply the distributive property:** $$(-1)(3) + (-1)(-4p) + (2p)(3) + (2p)(-4p)$$ 4. **Calculate each term:** $$-3 + 4p + 6p - 8p^2$$ 5. **Combine like terms:** $$-3 + (4p + 6p) - 8p^2 = -3 + 10p - 8p^2$$ 6. **Write the polynomial in standard form (descending powers):** $$-8p^2 + 10p - 3$$ **Final answer:** $$-8p^2 + 10p - 3$$