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.

(6a)(9ab) + (9a²)(5b)
(6 x 9)(a x a x b) + (9 x 5)(a² x b)
(54)(a¹⁺¹ x b) + (45)(a²b)
54a²b + 45a²b
99a²b

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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 3

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 = 3² + 3²
c² = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)

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).

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).

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² + 8y - 9 = 0
(y - 1)(y + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 1) or (y + 9) must equal zero:

If (y - 1) = 0, y must equal 1
If (y + 9) = 0, y must equal -9

So the solution is that y = 1 or -9