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

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.

(3a)(4ab) - (6a²)(6b)
(3 x 4)(a x a x b) - (6 x 6)(a² x b)
(12)(a¹⁺¹ x b) - (36)(a²b)
12a²b - 36a²b
-24a²b

When solving an equation with two variables, 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.)

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.

(6a)(2ab) + (5a²)(3b)
(6 x 2)(a x a x b) + (5 x 3)(a² x b)
(12)(a¹⁺¹ x b) + (15)(a²b)
12a²b + 15a²b
27a²b

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, \(c = \sqrt{a + b}\)