Determine the coefficient of x^3 in the expansion of (1 – x)^5(1 + 1/x)^5

Notice that

(1 - x)⁵ (1 + 1/x)⁵ = ((1 - x) (1 + 1/x))⁵ = (1 - x + 1/x - 1)⁵ = (1/x - x)⁵

Recall the binomial theorem:

Let a = 1/x, b = -x, and n = 5. Then

We get an x ³ term for

2k - 5 = 3   ==>   2k = 8   ==>   k = 4

so that the coefficient would be

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m