You notice that a certain rule is repeated three

You notice that a certain rule is repeated three times to distribute the first polynomial over the
second polynomial.
Then, the expression obtained in each step can be expanded using the algorithmic method.
The expression from the Step 1: x(ab + bc + ac) = xab +
4. x is multiplied by the first term of
the second polynomial
xbc +
5. x is multiplied by the second term of
the second polynomial
xac
6. x is multiplied by the first term of
the second polynomial
Applying Steps 4 ‐ 6 to the expressions obtained in Steps 2 and 3, we get:
7. y(ab + bc + ac) = yab + ybc + yac
8. z(ab + bc + ac) = zab + zbc + zac
Finally, we can put together all the distributions from Steps 4 ‐ 8, to find the outcome of the
product of two polynomials as follows:
(x + y + z)(ab + bc + ac + abc) = xab + xbc + xac + yab + ybc + yac + zab + zbc + zac
Applying Concepts and Principles: Sometimes when solving a problem we do not have a well ‐
defined algorithm, a formula, or a certain method. But we can put some of these methods and
different concepts and principles together to build a solution process for the problem.
For example:
Assume that D = 180(n ‒ 2) is the sum of all the interior angles of a regular polygon with n sides.
Now, we increase the number of the sides by 7, and want to know that how much the sum of
the interior angles in the new polygon is more than the original one.
We do not have an algorithm or a particular formula to find such an increase. Rather we can use
the concept of the variation in an equation.
Let’s say D
1
= Sum of the interior angles of the original polygon
D
2
= Sum of the interior angles of the new polygon with 7 more sides.
Then,
D
1
= 180(n ‒ 2)
= 180n ‒ 360
Now, we must replace n with (n + 7)

PERT - A Math Study Guide
All Rights Reserved
D
2
= 180[(n + 7) ‒ 2]
= 180(n + 5)
= 180n + 900
Next, subtract D
1
from D
2
to find the increase
D
2
‒ D
1
= (180n + 900) ‒ (180n ‒ 360)
= 180n + 900 ‒ 180n + 360
= 900 + 360
= 1260 degrees increase
13. Translate between Lines and Equations
As you see some sample points on the coordinate plane below, there are infinite number of
such points on a coordinate plane.
Each point is identified by two distances:
Distance from the horizontal axis or the x ‐ axis
Distance from the vertical axis or the y ‐ axis.
For example, the distance of the point A from x ‐ axis is 5 and from y ‐ axis is ‒ 4
These distances are called the coordinates of the point A and are denoted by ( ‒ 4, 5)