\ The distance from Newtown to Oldtown on the highway is (6x^2 + 2x - 2) miles, Using the back roads, the distance is (5x^2 - 8x - 6) miles. How many miles shorter is the second route?
11x^2 + 10x - 8
-x^2 - 6x + 4
x^2 + 10x + 4
x^2 - 6x - 8
To find the difference, 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, we get:
6x^2 + 2x - 2 - 5x^2 + 8x + 6
Combining like terms, we get:
x^2 + 10x + 4
Therefore, the answer is:
x^2 + 10x + 4
So the second route is x^2 + 10x + 4 miles shorter than the highway route.
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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.
Distance on the highway = 6x^2 + 2x - 2
Distance on the back roads = 5x^2 - 8x - 6
Now, let's subtract the distance on the back roads from the distance on the highway:
(6x^2 + 2x - 2) - (5x^2 - 8x - 6)
Removing the parentheses, we get:
6x^2 + 2x - 2 - 5x^2 + 8x + 6
Combining like terms, we have:
(6x^2 - 5x^2) + (2x + 8x) + (-2 + 6)
Simplifying further, we get:
x^2 + 10x + 4
Therefore, the second route is x^2 + 10x + 4 miles shorter than the first route.
To find the difference in distance between the two routes, we need to subtract the distance of the second route from the distance of the first route.
The distance from Newtown to Oldtown on the highway is given by the expression 6x^2 + 2x - 2 miles, and the distance using the back roads is given by the expression 5x^2 - 8x - 6 miles.
To find the difference, we subtract the distance on the back roads from the distance on the highway:
(6x^2 + 2x - 2) - (5x^2 - 8x - 6)
Distributing the negative sign:
6x^2 + 2x - 2 - 5x^2 + 8x + 6
Combine like terms:
(6x^2 - 5x^2) + (2x + 8x) + (-2 + 6)
Simplify:
x^2 + 10x + 4
Therefore, the second route is x^2 + 10x + 4 miles shorter than the first route.