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

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

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 1² + 4²
c² = 1 + 16
c² = 17
c = \( \sqrt{17} \)

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² - 6b - 45 = -5b - 3
b² - 6b - 45 + 3 = -5b
b² - 6b + 5b - 42 = 0
b² - b - 42 = 0

Next, factor the quadratic equation:

b² - b - 42 = 0
(b + 6)(b - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 6) or (b - 7) must equal zero:

If (b + 6) = 0, b must equal -6
If (b - 7) = 0, b must equal 7

So the solution is that b = -6 or 7

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 = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

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 = 1² + 1²
c² = 2
c = \( \sqrt{2} \)