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.

(4a)(8ab) + (9a²)(9b)
(4 x 8)(a x a x b) + (9 x 9)(a² x b)
(32)(a¹⁺¹ x b) + (81)(a²b)
32a²b + 81a²b
113a²b

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

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 - 5)(y + 4)
(y x y) + (y x 4) + (-5 x y) + (-5 x 4)
y² + 4y - 5y - 20
y² - y - 20

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{36} \) = 6

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 6² + 6²
c² = 72
c = \( \sqrt{72} \) = \( \sqrt{36 x 2} \) = \( \sqrt{36} \) \( \sqrt{2} \)
c = 6\( \sqrt{2} \)