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 fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.

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

\( \frac{7 x 5}{4 x 5} \) - \( \frac{9 x 2}{10 x 2} \)

\( \frac{35}{20} \) - \( \frac{18}{20} \)

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

\( \frac{35 - 18}{20} \) = \( \frac{17}{20} \) = \(\frac{17}{20}\)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (2 + 5) ÷ 3 x 3 - 2²
P: 2 + (7) ÷ 3 x 3 - 2²
E: 2 + 7 ÷ 3 x 3 - 4
MD: 2 + \( \frac{7}{3} \) x 3 - 4
MD: 2 + \( \frac{21}{3} \) - 4
AS: \( \frac{6}{3} \) + \( \frac{21}{3} \) - 4
AS: \( \frac{27}{3} \) - 4
AS: \( \frac{27 - 12}{3} \)
\( \frac{15}{3} \)
5

To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{52} \) = \( \frac{\frac{24}{4}}{\frac{52}{4}} \) = \( \frac{6}{13} \)

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

2\( \sqrt{5} \) x 6\( \sqrt{5} \)
(2 x 6)\( \sqrt{5 \times 5} \)
12\( \sqrt{25} \)

Now we need to simplify the radical:

12\( \sqrt{25} \)
12\( \sqrt{5^2} \)
(12)(5)
60