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) - (4a²)(5b)
(6 x 2)(a x a x b) - (4 x 5)(a² x b)
(12)(a¹⁺¹ x b) - (20)(a²b)
12a²b - 20a²b
-8a²b

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.

4a⁵ - 8a⁵ = -4a⁵

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 - 2)(y + 5)
(y x y) + (y x 5) + (-2 x y) + (-2 x 5)
y² + 5y - 2y - 10
y² + 3y - 10

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 36 as well and sum (Inside, Outside) to equal 13. For this problem, those two numbers are 4 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 13y + 36
y² + (4 + 9)y + (4 x 9)
(y + 4)(y + 9)

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 + 2a = 11a