1. The problem is to verify the equality of the expressions: $$(5 \times 8) \times 2 = 2 \times (20 \times 2)$$ and explore equivalent expressions. 2. Calculate the left side: $$(5 \times 8) \times 2 = 40 \times 2 = 80$$. 3. Calculate the right side: $$2 \times (20 \times 2) = 2 \times 40 = 80$$. 4. Both sides equal 80, so the equality holds. 5. Next, check the expression: $$(5 \times 8) \times 2 = 2 \times (5 \times 8)$$. 6. Calculate the right side: $$2 \times (5 \times 8) = 2 \times 40 = 80$$, which matches the left side. 7. Then, check: $$(5 \times 8) \times 2 = 5 \times (8 \times 2)$$. 8. Calculate the right side: $$5 \times (8 \times 2) = 5 \times 16 = 80$$, which matches the left side. 9. Finally, check: $$(5 \times 8) \times 2 = 5 \times (16 \times 1)$$. 10. Calculate the right side: $$5 \times (16 \times 1) = 5 \times 16 = 80$$, which matches the left side. 11. All expressions are equal to 80, demonstrating the associative and commutative properties of multiplication. Final answer: All given expressions equal 80.