When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

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 = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

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)(4ab) - (8a²)(4b)
(8 x 4)(a x a x b) - (8 x 4)(a² x b)
(32)(a¹⁺¹ x b) - (32)(a²b)
32a²b - 32a²b
0a²b

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).