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

\( \frac{-9c^6}{8c^2} \)
\( \frac{-9}{8} \) c^{(6 - 2)}
-1\(\frac{1}{8}\)c⁴

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{20\sqrt{4}}{4\sqrt{2}} \)
\( \frac{20}{4} \) \( \sqrt{\frac{4}{2}} \)
5 \( \sqrt{2} \)

The equation for this sequence is:

a_n = a_n-1 + 3(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.