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.

(4a)(6ab) - (5a²)(9b)
(4 x 6)(a x a x b) - (5 x 9)(a² x b)
(24)(a¹⁺¹ x b) - (45)(a²b)
24a²b - 45a²b
-21a²b

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 0. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 3) and (2, -3) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -1\(\frac{1}{2}\)x + 0

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 6 x 5) + (2 x 5 x 3) + (2 x 6 x 3)
sa = (60) + (30) + (36)
sa = 126

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

9b(b - y)
9(6)(6 - 4)
9(6)(2)
(54)(2)
108