Like Terms

To be successful in algebra, you must know how to identify terms and how to simplify (which would involve the distributive property and collecting like terms.)  The distributive property is not difficult, but until you train your eyes to look for signs … it can be a pretty tricky operation!  You must multiply the number and the sign that precedes a parenthesis by all numbers (including the signs) within that parenthesis.  When you are first learning, it may be helpful to give yourself plenty of room to see the terms of the expression.  For example,  would look simpler if you would space out each term so that you could see where the terms begin and end.  Then the expression would look like this …

           ... see how much easier it looks! J

There are four terms in this expression, namely … , , , and  .

The distributive property would have to be performed on both the second and fourth terms (since these terms contain parentheses.)  In the second term  (which is the coefficient of the term) would multiply both the   and the  .  It would look like this …

      .  Notice the sign changes.  Likewise in the fourth term,       .  The expression would now look like .  Again this looks crowded to me!  So give yourself some “breathing room” between the terms so that you can see which of them are like terms that can be combined to simplify the expression.  Here’s what the expression would look like with new spacing …

                      …

Like terms are terms which have the same variable parts.  In other words, beyond the coefficient (which is the number that sits in front of the term) the variable or variables (if there is more than one) have to be exactly alike … same letter/s, same exponent/s.  We can combine the terms , , , and , since they all have an “” after the coefficient.  This involves adding or subtracting the coefficients … .   would then be the new coefficient for the “” term.  Combing the  and  would produce  (since they are both constant terms, then they are like terms which can be combined).

The result would be  =    as the simplification of the above expression.