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

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 radicals, divide the coefficients and radicands separately:

\( \frac{25\sqrt{28}}{5\sqrt{4}} \)
\( \frac{25}{5} \) \( \sqrt{\frac{28}{4}} \)
5 \( \sqrt{7} \)

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{56} \) = \( \frac{\frac{36}{4}}{\frac{56}{4}} \) = \( \frac{9}{14} \)

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:

\( \frac{5c^5}{9c^2} \)
\( \frac{5}{9} \) c^{(5 - 2)}
\(\frac{5}{9}\)c³