Question

(Will Medal)
It has totally slipped my mind but can someone explain what are and how to identify terms in a expression?

Answer 1

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).

Answer 2

This is just 1 example

Answer 3

Want more examples?

Answer 4

Yes, please!

Answer 5

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.

\(\Large\color{black}{ \displaystyle \color{brown}{1}\color{blue}{-3x^4}\color{teal }{+5x^4}\color{magenta}{-11x}\color{darkgoldenrod}{+x^{1000}} }\)

Answer 6

each color is for a different terms

Answer 7

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.

Answer 8

As you read I will do one more example, and then perhaqps if we find that necessary I do more examples.

Answer 9

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.)

Answer 10

When you are done reading I will give you a short exercise.

Answer 11

i will put it up now, so that you can do it right away as you get to it.

Answer 12

`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? \(\large\color{black}{ \displaystyle 3w^{10} -2w^{10}+w-x}\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, red ,border:2px solid ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Answer 13

(I will be back after replies as soon as I can)

Answer 14

Q1:3?
Q2:2?
Q3:2?

Answer 15

for question 1, it has 4 terms
\(\Large\color{black}{ \displaystyle \color{purple}{x^3}\color{magenta}{-x^2}\color{brown}{+x}\color{gray}{+2} }\)

Answer 16

question 2, is correct. There are 2 terms.
(well done)

Answer 17

So the last one is 4 too?

Answer 18

yup, I was just about to say there are 4 terms in question 3. Very nice !!

Answer 19

Thanks you! :) I get it now! You're really awesome!

Answer 20

Just some colors and your quick understanding has made it:)
You are welcome!