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?
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.