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 -6 as well and sum (Inside, Outside) to equal 1. For this problem, those two numbers are -2 and 3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + y - 6
y² + (-2 + 3)y + (-2 x 3)
(y - 2)(y + 3)

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.

(5a)(4ab) - (8a²)(8b)
(5 x 4)(a x a x b) - (8 x 8)(a² x b)
(20)(a¹⁺¹ x b) - (64)(a²b)
20a²b - 64a²b
-44a²b

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

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.

8a x 2b = (8 x 2) (a x b) = 16ab