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.

(6a)(2ab) - (5a²)(4b)
(6 x 2)(a x a x b) - (5 x 4)(a² x b)
(12)(a¹⁺¹ x b) - (20)(a²b)
12a²b - 20a²b
-8a²b

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -9 as well and sum (Inside, Outside) to equal 0. For this problem, those two numbers are -3 and 3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 9
y² + (-3 + 3)y + (-3 x 3)
(y - 3)(y + 3)

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

sa = 2πr² + 2πrh
sa = 2π(3²) + 2π(3 x 3)
sa = 2π(9) + 2π(9)
sa = (2 x 9)π + (2 x 9)π
sa = 18π + 18π
sa = 36π