Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

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.

4a x 8b = (4 x 8) (a x b) = 32ab

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 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.

4c + 9 < -1 + 8c
4c < -1 + 8c - 9
4c - 8c < -1 - 9
-4c < -10
c < \( \frac{-10}{-4} \)
c < 2\(\frac{1}{2}\)

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 - 6)
(y x y) + (y x -6) + (-6 x y) + (-6 x -6)
y² - 6y - 6y + 36
y² - 12y + 36