To subtract these radicals together their radicands must be the same:

8\( \sqrt{175} \) - 9\( \sqrt{7} \)
8\( \sqrt{25 \times 7} \) - 9\( \sqrt{7} \)
8\( \sqrt{5^2 \times 7} \) - 9\( \sqrt{7} \)
(8)(5)\( \sqrt{7} \) - 9\( \sqrt{7} \)
40\( \sqrt{7} \) - 9\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{68} \) = \( \frac{\frac{36}{4}}{\frac{68}{4}} \) = \( \frac{9}{17} \)

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{32}{6} \) = 5\(\frac{1}{3}\)

So, it will take 5 full vans and one partially full van to transport the entire team making a total of 6 vans.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-2c³ - 7c³
(-2 - 7)c³
-9c³