A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

To subtract these radicals together their radicands must be the same:

8\( \sqrt{45} \) - 8\( \sqrt{5} \)
8\( \sqrt{9 \times 5} \) - 8\( \sqrt{5} \)
8\( \sqrt{3^2 \times 5} \) - 8\( \sqrt{5} \)
(8)(3)\( \sqrt{5} \) - 8\( \sqrt{5} \)
24\( \sqrt{5} \) - 8\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

First, solve for \( \left|c - 7\right| \):

\( \left|c - 7\right| \) + 7 = 6
\( \left|c - 7\right| \) = 6 - 7
\( \left|c - 7\right| \) = -1

The value inside the absolute value brackets can be either positive or negative so (c - 7) must equal - 1 or --1 for \( \left|c - 7\right| \) to equal -1:

So, c = 8 or c = 6.

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:

-6y⁷ - 2y⁷
(-6 - 2)y⁷
-8y⁷

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.