anonymous
  • anonymous
(Will Medal) It has totally slipped my mind but can someone explain what are and how to identify terms in a expression?
Mathematics
chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
lets consider the following: \(\large\color{black}{ \displaystyle x^3+2x-4 }\). Now, I will put each term in it's own color. \(\large\color{black}{ \displaystyle \color{blue}{x^3}\color{green}{+2x}\color{red}{-4} }\) (there are 3 terms) Why are they different terms? Because one variable is raised to a power of a 3. The other variable is raised to the power of 1 (as x and x¹ is same). And the third term is a a constant (constant - number that is not a variable).
SolomonZelman
  • SolomonZelman
This is just 1 example
SolomonZelman
  • SolomonZelman
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anonymous
  • anonymous
Yes, please!
SolomonZelman
  • SolomonZelman
can be like terms too \(\large\color{black}{ \displaystyle 1-3x^4+5x^4-11x+x^{1000} }\) the like terms are the terms that can be added (if they are of a same variable, and are raised to the same power. In this case like terms are 3x\(^4\) and 5x\(^4\) because they are same variable (x) and raised to same power (power of 4), and just like ` ` -3a+5a ` ` is 2a, so this, ` ` -3x\(^4\)+5x\(^4\) ` ` is equal to 2x\(^2\). But if there are not combined yet, they are considered to be different terms.) let me do the coloring for each term this time as well. \(\Large\color{black}{ \displaystyle \color{brown}{1}\color{blue}{-3x^4}\color{teal }{+5x^4}\color{magenta}{-11x}\color{darkgoldenrod}{+x^{1000}} }\)
SolomonZelman
  • SolomonZelman
each color is for a different terms
SolomonZelman
  • SolomonZelman
you can see that the 2nd term in blue, and the 3rd term in green-ish color, they can be added together, because they are like terms (same power and same variable), BUT before they are combined they are treated as separate terms.
SolomonZelman
  • SolomonZelman
As you read I will do one more example, and then perhaqps if we find that necessary I do more examples.
SolomonZelman
  • SolomonZelman
Now, I am going to show an example of a different variables in one expression. \(\Large\color{black}{ \displaystyle -x^4+w^4 }\) there two terms \(\Large\color{black}{ \displaystyle \color{red}{-x^4}\color{blue}{+w^4} }\) (they have the same power, but can't be added, because one is w and the other is x - different variables. They are different terms.) (Note: Again, even if I was able to combine them by adding or subtraction, BEFORE I HAVE DONE SO, they would be treated as different terms.)
SolomonZelman
  • SolomonZelman
When you are done reading I will give you a short exercise.
SolomonZelman
  • SolomonZelman
i will put it up now, so that you can do it right away as you get to it.
SolomonZelman
  • SolomonZelman
`Question #1:` How many terms are there is the following expression? \(\large\color{black}{ \displaystyle x^3-x^2+x+2 }\) \(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, red ,border:2px solid ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\) `Question #2:` How many terms are there is the following expression? \(\large\color{black}{ \displaystyle 4x+2a }\) \(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, red ,border:2px solid ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\) `Question #3:` How many terms are there is the following expression? \(\large\color{black}{ \displaystyle 3w^{10} -2w^{10}+w-x}\) \(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, red ,border:2px solid ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)
SolomonZelman
  • SolomonZelman
(I will be back after replies as soon as I can)
anonymous
  • anonymous
Q1:3? Q2:2? Q3:2?
SolomonZelman
  • SolomonZelman
for question 1, it has 4 terms \(\Large\color{black}{ \displaystyle \color{purple}{x^3}\color{magenta}{-x^2}\color{brown}{+x}\color{gray}{+2} }\)
SolomonZelman
  • SolomonZelman
question 2, is correct. There are 2 terms. (well done)
anonymous
  • anonymous
So the last one is 4 too?
SolomonZelman
  • SolomonZelman
yup, I was just about to say there are 4 terms in question 3. Very nice !!
anonymous
  • anonymous
Thanks you! :) I get it now! You're really awesome!
SolomonZelman
  • SolomonZelman
Just some colors and your quick understanding has made it:) You are welcome!

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