To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 6)(y - 3)
(y x y) + (y x -3) + (6 x y) + (6 x -3)
y² - 3y + 6y - 18
y² + 3y - 18

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 first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² - 3y - 54 = 0
(y + 6)(y - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 6) or (y - 9) must equal zero:

If (y + 6) = 0, y must equal -6
If (y - 9) = 0, y must equal 9

So the solution is that y = -6 or 9

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 < sign and the answer on the other.

b - 9 < \( \frac{b}{-1} \)
-1 x (b - 9) < b
(-1 x b) + (-1 x -9) < b
-b + 9 < b
-b + 9 - b < 0
-b - b < -9
-2b < -9
b < \( \frac{-9}{-2} \)
b < 4\(\frac{1}{2}\)

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.