Operation of Algebraic Expression

Before we see how to add and subtract integers, we define terms and factors.

Terms and Factors

A term in an algebraic expression is an expression involving letters and/or numbers (called factors), multiplied together.

Example
The algebraic expression

5x

is an example of one single term. It has factors 5 and x.

The 5 is called the coefficient of the term and the x is a variable.

Like Terms

"Like terms" are terms that contain the same variables raised to the same power.

Example
3x and 7x are like terms.

Adding and Subtracting Terms

Important: We can only add or subtract like terms.

Why? Think of it like this. On a table we have 4 pencils and 2 books. We cannot add the 4 pencils to the 2 books - they are not the same kind of object.

We go get another 3 pencils and 6 books. Altogether we now have 7 pencils and 8 books. We can't combine these quantities, since they are different types of objects.

Next, our sister comes in and grabs 5 pencils. We are left with 2 pencils and we still have the 8 books.

Similarly with algebra, we can only add (or subtract) similar "objects", or those with the same letter raised to the same power.

Example
Simplify 13x + 7y − 2x + 6a

13x + 7y − 2x + 6a

The only like terms in this expression are 13x and −2x. We cannot do anything with the 7y or 6a.

So we group together the terms we can subtract, and just leave the rest:

(13x − 2x) + 6a + 7y

= 6a + 11x + 7y

We usually present our variables in alphabetical order, but it is not essential.

Multiplication of Algebraic Expressions

When we multiply algebraic expressions, we need to remember the Index Laws from the Numbers chapter.

Let's see how algebra multiplication works with a series of examples.

Example
Multiply (x + 5)(a − 6)

We multiply this out as follows. We take each term of the first bracket and multiply them by the second bracket. Then we expand out the result.

(x + 5)(a − 6)

= x(a − 6) + 5(a − 6)

= ax − 6x + 5a − 30

We cannot do any more with this answer. There are no like terms, so we cannot simplify it in any way.

Dividing by a Fraction

Recall the following when dividing algebraic expressions.

The reciprocal of a number x, is 1/x

For example, the reciprocal of 5 is 1/5 and the reciprocal of 5/3 is 3/5

To divide by a fraction, you multiply by the reciprocal of the fraction.




This article was originally published on The Interactive Mathematics. Read the original article.

Source:
https://www.intmath.com/basic-algebra/1-addition-subtraction-algebra.php

https://www.intmath.com/basic-algebra/2-multiplication-algebra.php

https://www.intmath.com/basic-algebra/3-division-algebra.php