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 x 9b = (8 x 9) (a x b) = 72ab

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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

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

x² - 4x + 4 = 0
(x - 2)(x - 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (x - 2) must equal zero:

If (x - 2) = 0, x must equal 2

So the solution is that x = 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:

(y - 5)(y - 5)
(y x y) + (y x -5) + (-5 x y) + (-5 x -5)
y² - 5y - 5y + 25
y² - 10y + 25