the distance from Newtown to oldtown on the highway is (6x^2 + 2x - 2) miles. using the back roads, the distant is (5x^2 - 8x - 6) miles. how many miles shorter is the second route?

Answer 1

To find the difference in distance between the two routes, we need to subtract the distance on the back roads from the distance on the highway:

(6x^2 + 2x - 2) - (5x^2 - 8x - 6)

Simplifying the expression, we get:

6x^2 + 2x - 2 - 5x^2 + 8x + 6

Combining like terms, we get:

x^2 + 10x + 4

This expression represents the difference in distance between the two routes. We cannot simplify it any further, so the answer is:

x^2 + 10x + 4 miles shorter on the back roads.