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.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-3c⁷ x 7c⁵
(-3 x 7)c^{(7 + 5)}
-21c¹²

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:

3y⁴ - 7y⁴
(3 - 7)y⁴
-4y⁴

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:

\( \frac{3 x 5}{4 x 5} \) - \( \frac{4 x 2}{10 x 2} \)

\( \frac{15}{20} \) - \( \frac{8}{20} \)

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

\( \frac{15 - 8}{20} \) = \( \frac{7}{20} \) = \(\frac{7}{20}\)