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

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{6 x 3}{2 x 3} \) - \( \frac{7 x 1}{6 x 1} \)

\( \frac{18}{6} \) - \( \frac{7}{6} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{18 - 7}{6} \) = \( \frac{11}{6} \) = 1\(\frac{5}{6}\)

The factors of a number are all positive integers that divide evenly into the number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

3c³ x 7c³
(3 x 7)c^{(3 + 3)}
21c⁶

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.