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

3 + (2 + 2) ÷ 4 x 5 - 5²
P: 3 + (4) ÷ 4 x 5 - 5²
E: 3 + 4 ÷ 4 x 5 - 25
MD: 3 + \( \frac{4}{4} \) x 5 - 25
MD: 3 + \( \frac{20}{4} \) - 25
AS: \( \frac{12}{4} \) + \( \frac{20}{4} \) - 25
AS: \( \frac{32}{4} \) - 25
AS: \( \frac{32 - 100}{4} \)
\( \frac{-68}{4} \)
-17

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

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{4 x 4}{6 x 4} \) - \( \frac{5 x 3}{8 x 3} \)

\( \frac{16}{24} \) - \( \frac{15}{24} \)

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

\( \frac{16 - 15}{24} \) = \( \frac{1}{24} \) = \(\frac{1}{24}\)

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.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.