A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

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 volume of a cube is height x length x width:

v = h x l x w
v = 1 x 3 x 9
v = 27

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.

(7a)(6ab) + (2a²)(9b)
(7 x 6)(a x a x b) + (2 x 9)(a² x b)
(42)(a¹⁺¹ x b) + (18)(a²b)
42a²b + 18a²b
60a²b

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 7 as well and sum (Inside, Outside) to equal -8. For this problem, those two numbers are -7 and -1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 8y + 7
y² + (-7 - 1)y + (-7 x -1)
(y - 7)(y - 1)