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.

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with z° = 12, the value of a° is 12.

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:

z² - 5z - 38 = -2z + 2
z² - 5z - 38 - 2 = -2z
z² - 5z + 2z - 40 = 0
z² - 3z - 40 = 0

Next, factor the quadratic equation:

z² - 3z - 40 = 0
(z + 5)(z - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 5) or (z - 8) must equal zero:

If (z + 5) = 0, z must equal -5
If (z - 8) = 0, z must equal 8

So the solution is that z = -5 or 8

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 20 as well and sum (Inside, Outside) to equal 9. For this problem, those two numbers are 4 and 5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 9y + 20
y² + (4 + 5)y + (4 x 5)
(y + 4)(y + 5)

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 6 x 5
a = 30