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.

(5a)(9ab) - (3a²)(6b)
(5 x 9)(a x a x b) - (3 x 6)(a² x b)
(45)(a¹⁺¹ x b) - (18)(a²b)
45a²b - 18a²b
27a²b

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(9 + 9)(4)
a = ½(18)(4)
a = ½(72) = \( \frac{72}{2} \)
a = 36

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 32° - 31° = 117°

So, d° = 31° + 117° = 148°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 32° = 148°

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

4a - 8 < 4 + 6a
4a < 4 + 6a + 8
4a - 6a < 4 + 8
-2a < 12
a < \( \frac{12}{-2} \)
a < -6