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

-2b⁵ + 4b⁵
(-2 + 4)b⁵
2b⁵

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

7\( \sqrt{28} \) - 5\( \sqrt{7} \)
7\( \sqrt{4 \times 7} \) - 5\( \sqrt{7} \)
7\( \sqrt{2^2 \times 7} \) - 5\( \sqrt{7} \)
(7)(2)\( \sqrt{7} \) - 5\( \sqrt{7} \)
14\( \sqrt{7} \) - 5\( \sqrt{7} \)

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

The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 have in common.

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 20 workers at the company now and that's enough to staff 5 crews so there are \( \frac{20}{5} \) = 4 workers on a crew. 10 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 10 x 4 = 40 total workers to staff the crews during the busy season. The company already employs 20 workers so they need to add 40 - 20 = 20 new staff for the busy season.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).