Messing with Dimensions

I have a question for you all:

Why can't we subtract cm from cm^2 ?

It is confusing why schools told us to subtract like terms and not unlike terms. Well cm^2 is cm*cm so it composes of cm.

I think it is related to algebra like y^2-y where y^2 is y times y but we can't do anything with y because y^2=y times y and not subtraction. But y^2-y gives you some answer.

This is also related to imaginary numbers. i^2=-1. But -1-i=something confusing. So I keep my roots on imaginary than algebra.

can anyone help me clear my confusion for the above problem.

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Comments

If $y$ is any integer or real number then $y^2 - y = y(y - 1)$ . It is the product of two consecutive integers or any two real numbers $y$ and $y - 1$ so you will definitely get answer.

Ram Mohith - 2 years, 10 months ago

But say for example we have 4cm^2 - 8cm

Mohammad Farhat - 2 years, 10 months ago

It just of the form : $Area - Perimeter$ .

Ram Mohith - 2 years, 10 months ago

@Ram Mohith – oh

Mohammad Farhat - 2 years, 10 months ago

@Ram Mohith – Is it possible to get a more simplified result

Mohammad Farhat - 2 years, 10 months ago

@Mohammad Farhat – Not possible. If it is mentioned that $cm$ is not any unit and it is just a constant then the simplified form will be $4cm(cm - 2)$

Ram Mohith - 2 years, 10 months ago

@Ram Mohith – oh

Mohammad Farhat - 2 years, 10 months ago

We can cancel out or add any two like terms if and only if both the like terms are of the same degree.

$Ex : 5y - 3y = 2y$ . Here $5y$ and $3y$ are of same degree that is $1$ so you can subtract them or you can add them .

But what about $(x^3 - x)$ ?

Solution : You cannot subtract them nor you can add them. The reason is that the first $x$ is of the degree $3$ where as the second $x$ is of the degree $1$ .

What about $y^3 - y^2 + 5y + 2y + 3$ ?

Solution : You cannot add or subtract $y^3$ and $y^2$ because there of different degree : $3$ and $2$ respectively. Coming to $5y$ and $2y$ they are of same degree $1$ so they add up to become $7y$ . Now again $y^3,y^2,7y ~and~3$ cannot be added because they are of different degrees $3,2,1,0$ respectively.

Coming to $x^3 - y^3$ what will you say about this ?

Solution : Nothing can be done as they are unlike terms.

Mohammad Farhan you should be strong in these basic fundamentals for you to solve further higher questions.

Ram Mohith - 2 years, 10 months ago

Mohammad Farhat - 2 years, 10 months ago

Coming to the first part of the note your query itself is in an undetermined form . You should note that $cm,cm^2,cm^3,m^3,g,kg,etc$ are all units and they can neither be added nor subtracted nor multiplied nor any operation can be done. Don't be confused.

Ram Mohith - 2 years, 10 months ago

Lets go to the prime powers relationship

Mohammad Farhat - 2 years, 10 months ago

I have to award my mentor. What would you want

Mohammad Farhat - 2 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$