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)(4ab) + (3a²)(7b)
(5 x 4)(a x a x b) + (3 x 7)(a² x b)
(20)(a¹⁺¹ x b) + (21)(a²b)
20a²b + 21a²b
41a²b

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.

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

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 4 x 4) + (2 x 4 x 8) + (2 x 4 x 8)
sa = (32) + (64) + (64)
sa = 160

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

-5a + 4y = -3a + y + 2
-5a = -3a + y + 2 - 4y
-5a + 3a = y + 2 - 4y
-2a = -3y + 2
a = \( \frac{-3y + 2}{-2} \)
a = \( \frac{-3y}{-2} \) + \( \frac{2}{-2} \)
a = 1\(\frac{1}{2}\)y - 1

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.