(6) \( \quad(-2 x-4 y)(3 x+5 y) \cdot 2 \) (8) \( \quad\left(4 b^{2}+5 c^{2}\right)\left(-b^{3}+2 c^{5}\right) \)

Let's expand and simplify each of the given expressions step by step. --- ### Problem (6) \[ (-2x - 4y)(3x + 5y) \cdot 2 \] **Step 1: Expand the binomials** \[ \begin{align*} (-2x)(3x) &= -6x^2 \\ (-2x)(5y) &= -10xy \\ (-4y)(3x) &= -12xy \\ (-4y)(5y) &= -20y^2 \end{align*} \] Combine the like terms: \[ -6x^2 - 10xy - 12xy - 20y^2 = -6x^2 - 22xy - 20y^2 \] **Step 2: Multiply by 2** \[ 2 \cdot (-6x^2 - 22xy - 20y^2) = -12x^2 - 44xy - 40y^2 \] **Final Answer for Problem (6):** \[ -12x^2 - 44xy - 40y^2 \] --- ### Problem (8) \[ (4b^{2} + 5c^{2})(-b^{3} + 2c^{5}) \] **Step 1: Expand the binomials** \[ \begin{align*} 4b^{2} \cdot (-b^{3}) &= -4b^{5} \\ 4b^{2} \cdot 2c^{5} &= 8b^{2}c^{5} \\ 5c^{2} \cdot (-b^{3}) &= -5b^{3}c^{2} \\ 5c^{2} \cdot 2c^{5} &= 10c^{7} \end{align*} \] **Step 2: Combine all terms** \[ -4b^{5} - 5b^{3}c^{2} + 8b^{2}c^{5} + 10c^{7} \] **Final Answer for Problem (8):** \[ -4b^{5} - 5b^{3}c^{2} + 8b^{2}c^{5} + 10c^{7} \] --- These are the fully expanded forms of the given expressions.