Strategies, Sample Questions, and Random Ramblings.
July 18, 2015
Now it is time to start putting the pieces together. We have talked about some of the rules of how algebra works, but now we have to start applying some of these things in sets of information given.
Expression: a phrase that contains numbers, variables and operators (like, multiply, and divide).
Since we already know the order of operations and have had some work with variables, we are just going to jump right into some examples.
6(x-y) + 4x + 5y
The first thing to note is that the 6 must be distributed to both of the terms inside the parenthesis. This leaves us with the expression :
6x - 6y + 4x + 5y
When combining the x terms and the y terms, the result is the following:
10x - y
Yes, this is a very simplistic example, and they will get harder; however, it is important to remember that the rules we have learned will not change. Simply follow the road map and these questions will get easier and easier.
The operation that we performed with 6(x-y) is known as the distributive law. In other words, the value outside of the parenthesis must be multiplied by each term within the parenthesis. In practice it looks like this:
x(a+b) = ax + bx
This can also be done in reverse. Consider the following expression:
3x + 3y
Essentially, you can factor a 3 from each term in order to condense the expression. This can only be done when both terms can be divided by an identical number/variable; in this case ‘3’.
(3)x + (3)y = 3(x+y)
Greg R., client, New York City
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