The Sunday News
Topic: Algebra-Symbolic expression
Syllabus Objective: – (6.6.1) Express basic arithmetic processes in letter symbols;
Algebra is a branch of Mathematics that uses symbols to represent numbers. Formulation of Algebraic expressions is simply a process by which one interprets a word problem and derives a meaningful mathematical model for it.
In this article we are mainly focusing on the simplification of algebraic expressions as per the above syllabus objective. They are basically two ways in which we simplify algebraic expressions at O-level. These include:
Simplifying by grouping.
Expanding by removing brackets.
Simplifying by grouping
An expression is a sum or difference of two or more algebraic terms. Consider the two examples shown below:
16x-3x+4x-9x
6x-3y+4x-9y
The examples listed above are both expressions. The difference between them is that (a) can reduce to a single term (monomial) because the individual terms are all expressed in terms of one variable which has the same configuration (x) whereas (b) will reduce to as far as two terms (binomial) because its individual terms are expressed in terms of either (x or y).
Question
Simplify;
13x-3x+9x-11x.
9x-3y+7x-4y.
Solution:
As mentioned above, both (i) and (ii) are algebraic expressions in which we will employ the method of grouping to simplify.
Case (i)
In the first case (i), we have four terms that are interlinked by three operations (-,+ and-). If you would recall, in one of the articles on Directed Numbers we did mention that a minus (-) and a plus (+) are called even pair operations. By that we meant that in a case where terms are interlinked by a minus (-) and a plus (+) respectively there is no need to give precedence to the plus (+) operation. It would rather be easier to evaluate the expression sequentially. In the above case item (i) we could choose to evaluate the expression sequentially. This has a short coming especially when the expression has a large number of terms. As of the case in item (i) above, we would have to generate three sequences before getting to the answer. As a result we employ the method of grouping.
In the first case item (i) we would rearrange and group terms in terms of the signs (+and-). The rearranged expression should look like;
13x+9x-3x-11x
Beyond this stage the expression can further be simplified by combining the positives versus the negatives separately. Hence the expression reduces to;
22x-14x
The final answer reduces to the monomial (a single term) 8x.
Case (ii)
In item (ii) we can as well employ method of grouping to simplify the expression. However in this particular case we group terms in terms of their variables (i.e those expressed in terms of x versus those in terms of y) rather than grouping in terms of the signs (+ and -). Hence, after rearranging the expression in item (ii) reduces to;
9x+7x-3y-4y
The above terms have been paired in terms of like variables and configuration. They can be simplified separately and the expression reduces to;
16x-7y
NB Beyond this the expression cannot be further simplified because the individual terms are not like terms. As a result the solution is a Binomial expression (i.e a sum or difference of two terms).
Attempt the following:
Simplify
12x-17x+5x-7x.
8x+3y-2x+6y.
W. Ngwenya and T. Bosha are tutors at the Adult school of Mathematics. They can be reached on the Facebook page: Bulawayo Adult School of Mathematics.
Contact: (+263)774 318 368
(+263)718659763
