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.

(3a)(8ab) - (4a²)(6b)
(3 x 8)(a x a x b) - (4 x 6)(a² x b)
(24)(a¹⁺¹ x b) - (24)(a²b)
24a²b - 24a²b
0a²b

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 perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 15cm + 9cm + 7cm = 31cm

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 + 2z - 5 = 2z + 4
z² + 2z - 5 - 4 = 2z
z² + 2z - 2z - 9 = 0
z² - 9 = 0

Next, factor the quadratic equation:

z² - 9 = 0
(z - 3)(z + 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 3) or (z + 3) must equal zero:

If (z - 3) = 0, z must equal 3
If (z + 3) = 0, z must equal -3

So the solution is that z = 3 or -3

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 b° = 162, the value of w° is 18.