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 15 as well and sum (Inside, Outside) to equal 8. For this problem, those two numbers are 3 and 5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 8y + 15
y² + (3 + 5)y + (3 x 5)
(y + 3)(y + 5)

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)(7ab) + (2a²)(4b)
(3 x 7)(a x a x b) + (2 x 4)(a² x b)
(21)(a¹⁺¹ x b) + (8)(a²b)
21a²b + 8a²b
29a²b

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.

6a + 8a = 14a

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.

3a⁶ - 3a⁶ = 0a⁶

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) - (9a²)(3b)
(3 x 4)(a x a x b) - (9 x 3)(a² x b)
(12)(a¹⁺¹ x b) - (27)(a²b)
12a²b - 27a²b
-15a²b