You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

2b + 5x = 6b + 4x + 7
2b = 6b + 4x + 7 - 5x
2b - 6b = 4x + 7 - 5x
-4b = -x + 7
b = \( \frac{-x + 7}{-4} \)
b = \( \frac{-x}{-4} \) + \( \frac{7}{-4} \)
b = \(\frac{1}{4}\)x - 1\(\frac{3}{4}\)

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\( \sqrt{2} \)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

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