You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-8a + 1 = \( \frac{a}{2} \)
2 x (-8a + 1) = a
(2 x -8a) + (2 x 1) = a
-16a + 2 = a
-16a + 2 - a = 0
-16a - a = -2
-17a = -2
a = \( \frac{-2}{-17} \)
a = \(\frac{2}{17}\)

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(2ab) + (4a²)(2b)
(8 x 2)(a x a x b) + (4 x 2)(a² x b)
(16)(a¹⁺¹ x b) + (8)(a²b)
16a²b + 8a²b
24a²b

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(3²) + 2π(3 x 8)
sa = 2π(9) + 2π(24)
sa = (2 x 9)π + (2 x 24)π
sa = 18π + 48π
sa = 66π