A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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

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

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

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:

6c² + 5c²
(6 + 5)c²
11c²

The number of students taking German or Spanish is 8 + 8 = 16. Of that group of 16, 5 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 5 = 11 who are taking at least one language. 19 - 11 = 8 students who are not taking either language.