What is the difference between 27x98 and 26x97? Explain how you know by multiplying.

I don't think you need to multiply here. Let me tell you an interesting trick to solving this problem.

Let 27 = x, and 98 = y. We know that 26 * 97 = (x-1) * (y-1)

Let us add 26 to 26 * 97. We would get 26 * 98 = (x-1) * y. Our first difference would be 26.

Now to get to 27*98 from 26 * 98, we just need to add 98. Therefore our second difference is 98.

Adding these two differences together, we get 26 + 98=124.

Sure enough, after multiplying these two values, we get 2646 and 2522, and their difference is 124.

27*98=2646 26*97=2522 2646-2522=124