To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

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 + 7)
(y x y) + (y x 7) + (-6 x y) + (-6 x 7)
y² + 7y - 6y - 42
y² + y - 42

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

9c - 8x = 7c - 5x + 8
9c = 7c - 5x + 8 + 8x
9c - 7c = -5x + 8 + 8x
2c = 3x + 8
c = \( \frac{3x + 8}{2} \)
c = \( \frac{3x}{2} \) + \( \frac{8}{2} \)
c = 1\(\frac{1}{2}\)x + 4

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

2c(c - y)
2(5)(5 - 6)
2(5)(-1)
(10)(-1)
-10

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).