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 12 as well and sum (Inside, Outside) to equal -8. For this problem, those two numbers are -6 and -2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 8y + 12
y² + (-6 - 2)y + (-6 x -2)
(y - 6)(y - 2)

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.

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.

(2a)(9ab) + (5a²)(9b)
(2 x 9)(a x a x b) + (5 x 9)(a² x b)
(18)(a¹⁺¹ x b) + (45)(a²b)
18a²b + 45a²b
63a²b

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

4a - 8y = 9a - 6y - 4
4a = 9a - 6y - 4 + 8y
4a - 9a = -6y - 4 + 8y
-5a = 2y - 4
a = \( \frac{2y - 4}{-5} \)
a = \( \frac{2y}{-5} \) + \( \frac{-4}{-5} \)
a = -\(\frac{2}{5}\)y + \(\frac{4}{5}\)

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.

5a⁴ + 7a⁴ = 12a⁴