1. **Stating the problem:** We need to solve the expression $$h^2 = (2 m^2 + 3)(4 m - 10)$$ for $h^2$ in terms of $m$. 2. **Formula and rules:** To simplify, we use the distributive property (also called FOIL for binomials): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply distributive property:** $$h^2 = (2 m^2 + 3)(4 m - 10) = 2 m^2 \times 4 m + 2 m^2 \times (-10) + 3 \times 4 m + 3 \times (-10)$$ 4. **Calculate each term:** $$2 m^2 \times 4 m = 8 m^3$$ $$2 m^2 \times (-10) = -20 m^2$$ $$3 \times 4 m = 12 m$$ $$3 \times (-10) = -30$$ 5. **Combine all terms:** $$h^2 = 8 m^3 - 20 m^2 + 12 m - 30$$ 6. **Final answer:** $$\boxed{h^2 = 8 m^3 - 20 m^2 + 12 m - 30}$$ This expression gives $h^2$ fully expanded in terms of $m$.