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.

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

\( \frac{-3x^7}{4x^2} \)
\( \frac{-3}{4} \) x^{(7 - 2)}
-\(\frac{3}{4}\)x⁵

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 50mph \times 7h \)
350 miles

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:

-9x² - 5x²
(-9 - 5)x²
-14x²

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

4 + (4 + 3) ÷ 4 x 5 - 2²
P: 4 + (7) ÷ 4 x 5 - 2²
E: 4 + 7 ÷ 4 x 5 - 4
MD: 4 + \( \frac{7}{4} \) x 5 - 4
MD: 4 + \( \frac{35}{4} \) - 4
AS: \( \frac{16}{4} \) + \( \frac{35}{4} \) - 4
AS: \( \frac{51}{4} \) - 4
AS: \( \frac{51 - 16}{4} \)
\( \frac{35}{4} \)
8\(\frac{3}{4}\)