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)(3ab) + (5a²)(9b)
(5 x 3)(a x a x b) + (5 x 9)(a² x b)
(15)(a¹⁺¹ x b) + (45)(a²b)
15a²b + 45a²b
60a²b

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

9a - 3a = 6a

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 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 - 3)(y - 9)
(y x y) + (y x -9) + (-3 x y) + (-3 x -9)
y² - 9y - 3y + 27
y² - 12y + 27