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 Combining like terms using
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to combine like terms using addition and subtraction. By the end of the module students should be able to combine like terms in an algebraic expression.
Section overview
Combining like terms
From our examination of terms in
[link] , we know that
like terms are terms in which the variable parts are identical. Like terms is an appropriate name since terms with identical variable parts and different numerical coefficients represent different amounts of the same quantity. When we are dealing with quantities of the same type, we may combine them using addition and subtraction.
Simplifying an algebraic expression
An algebraic expression may be
simplified by combining like terms.
This concept is illustrated in the following examples.

$\text{8 records}+\text{5 records}=\text{13 records}\text{.}$
Eight and 5 of the same type give 13 of that type. We have combined quantities of the same type.

$\text{8 records}+\text{5 records}+\text{3 tapes}=\text{13 records}+\text{3 tapes}\text{.}$
Eight and 5 of the same type give 13 of that type. Thus, we have 13 of one type and 3 of another type. We have combined only quantities of the same type.
 Suppose we let the letter
$x$ represent "record." Then,
$8x+5x=13x$ . The terms
$8x$ and
$5x$ are like terms. So, 8 and 5 of the same type give 13 of that type. We have combined like terms.
 Suppose we let the letter
$x$ represent "record" and
$y$ represent "tape." Then,
$8x+5x+3y=13x+5y$
We have combined only the like terms.
After observing the problems in these examples, we can suggest a method for simplifying an algebraic expression by combining like terms.
Combining like terms
Like terms may be combined by adding or subtracting their coefficients and affixing the result to the common variable.
Sample set a
Simplify each expression by combining like terms.
$3a+2b5a+a+6b\text{.}$ The like terms are
$\underset{7a}{\underset{35+1=7}{\underbrace{3a,\text{}5a,\text{}a}}}$
$\underset{8b}{\underset{2+6=8}{\underbrace{2b,\text{}6b}}}$
Thus,
$3a+2b5a+a+6b\text{=}7a+8b\text{.}$
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Practice set a
Simplify each expression by combining like terms.
Exercises
Simplify each expression by combining like terms.
Exercises for review
Questions & Answers
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is this allso about nanoscale material
Almas
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nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
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There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Application of nanotechnology in medicine
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Kamaluddeen
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Damian
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Professor
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Alexandre
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Damian
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What is meant by 'nano scale'?
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LITNING
scanning tunneling microscope
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Rafiq
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Rafiq
Rafiq
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Anam
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Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scientists to 52,000. How many were there in 1973?
7hours 36 min  4hours 50 min
Source:
OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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