Simplify the following expression. $$[(1\cdot2)+(3\cdot4)-(5\cdot6)+(7\cdot8)]\cdot(9\cdot0)$$
I notice that this expression is a product of two parts: the part in the square brackets and the part outside the brackets. I also notice that the part outside the brackets is 9 times 0, which is always 0. This means that the whole expression will be 0, regardless of what is inside the brackets. So I don't even need to simplify the part inside the brackets, because it will not affect the final answer. Therefore, the simplest way to write the expression is 0. 