The number of students taking German or Spanish is 5 + 8 = 13. Of that group of 13, 3 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 13 - 3 = 10 who are taking at least one language. 21 - 10 = 11 students who are not taking either language.

The greatest common factor (GCF) is the greatest factor that divides two integers.

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:

-4a⁶ - 8a⁶
(-4 - 8)a⁶
-12a⁶

The factors of a number are all positive integers that divide evenly into the number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).