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 + 6)
(y x y) + (y x 6) + (-2 x y) + (-2 x 6)
y² + 6y - 2y - 12
y² + 4y - 12

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 x 4b = (2 x 4) (a x b) = 8ab

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.

(8a)(8ab) + (7a²)(6b)
(8 x 8)(a x a x b) + (7 x 6)(a² x b)
(64)(a¹⁺¹ x b) + (42)(a²b)
64a²b + 42a²b
106a²b

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 10 as well and sum (Inside, Outside) to equal 7. For this problem, those two numbers are 2 and 5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 7y + 10
y² + (2 + 5)y + (2 x 5)
(y + 2)(y + 5)

A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.