1. **State the problem:** Simplify the expression $$2j(7j^2k^2 + jk^2 + 5k) - 9k(-2j^2k^2 + 2k^2 + 3j)$$. 2. **Distribute each term:** - Multiply $$2j$$ by each term inside the first parentheses: $$2j \times 7j^2k^2 = 14j^3k^2$$ $$2j \times jk^2 = 2j^2k^2$$ $$2j \times 5k = 10jk$$ - Multiply $$-9k$$ by each term inside the second parentheses: $$-9k \times -2j^2k^2 = 18j^2k^3$$ $$-9k \times 2k^2 = -18k^3$$ $$-9k \times 3j = -27jk$$ 3. **Rewrite the expression with distributed terms:** $$14j^3k^2 + 2j^2k^2 + 10jk + 18j^2k^3 - 18k^3 - 27jk$$ 4. **Group like terms:** - Terms with $$j^3k^2$$: $$14j^3k^2$$ - Terms with $$j^2k^2$$: $$2j^2k^2$$ - Terms with $$j^2k^3$$: $$18j^2k^3$$ - Terms with $$jk$$: $$10jk - 27jk = -17jk$$ - Terms with $$k^3$$: $$-18k^3$$ 5. **Final simplified expression:** $$14j^3k^2 + 2j^2k^2 + 18j^2k^3 - 17jk - 18k^3$$