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.

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:

8y⁴ + 1y⁴
(8 + 1)y⁴
9y⁴

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

\( \frac{24\sqrt{12}}{8\sqrt{6}} \)
\( \frac{24}{8} \) \( \sqrt{\frac{12}{6}} \)
3 \( \sqrt{2} \)

To simplify a radical, factor out the perfect squares:

\( \sqrt{18} \)
\( \sqrt{9 \times 2} \)
\( \sqrt{3^2 \times 2} \)
3\( \sqrt{2} \)

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.