Hey it’s Professor Dave, let’s learn some

algebraic properties. Remember when we learned about a few different

mathematical properties and how they pertained to numbers? Let’s learn how they will be important in

algebra when manipulating variables. The most important of these properties will

be the distributive property. This told us how a number could be distributed

across a parenthetical sum or difference. This didn’t matter too much for arithmetic,

because four times the quantity of two plus three is certainly equal to four times two

plus four times three, but there was nothing stopping us from adding two and three first,

and then multiplying by four. We should get twenty no matter which method

we choose. But with algebra, there are variables that

must remain as they are, and can’t be combined with numbers, so if we have four times the

quantity of two X plus three, the only other meaningful way to express this is by distributing

the four across the sum. That will give us four times two X plus four

times three, which will simplify to eight X plus twelve. In algebra, we will want to be able to use

the distributive property this way, and we will even want to be able to do it in reverse,

by removing some common factor from a sum or difference. For example, if we have three X squared plus

six X, another way to express this would involve identifying the greatest common factor of

these terms, and factoring it out of the expression. In this case, we can rewrite these as three

times X times X and two times three times X. Taking everything we find in both terms,

the greatest common factor would be three X, and if we pull a three X out of both terms,

meaning we divide each term by three X, we end up with the three X out here, and then

X plus two in parentheses. We can verify that this worked as expected

by then distributing the three X across the sum. Three X times X is three X squared, and three

X times two is six X. So we can use the distributive property in

a variety of ways to generate equivalent expressions. Other properties that also apply include the

commutative property for addition and multiplication. Two plus three is the same as three plus two,

and two times three is the same as three times two. If these become algebraic terms, the commutative

property applies in precisely the same way; the order in which we add or multiply algebraic

terms is irrelevant. Two X plus three is the same as three plus

two X, and two X times three is the same as three times two X. However, let’s recall that the commutative

property does not apply to subtraction or division, and that will be the case in algebra

as well. We also learned about the associative property,

and that will apply in algebra too, which we will find out later when we have to manipulate

equations with lots of terms in them. Changing the way these are grouped will not

matter if we are doing addition or multiplication. To be thorough, let’s also mention some

pretty intuitive properties like the additive identity property. This says that you can add or subtract zero

to any number or algebraic term, and it will retain its identity. Five plus zero is five. Three X minus zero is three X. Seems obvious,

but it will come in handy. The multiplicative identity property works

the same way except with the number one instead of zero. Any number or algebraic term times one will

give you the same term again. Four X times one is four X. And lastly, the inverse property of addition

says that anything plus its additive inverse equals zero, so X plus negative X equals zero,

and the inverse property of multiplication says that anything times its multiplicative

inverse equals one, so X times one over X equals one. That’s pretty much all we need to know in

terms of number properties for algebra, so let’s get to some equations.

## 19 Comments

## pramod m

Awesome sir

## Iron Armada

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## candis johnson

Good good ππ½ππ½

## Faisal Sa

Nice Job

## Kaleem Kaleem

Request for ray in maths about geometry

## Cole Left

πππ

## Abdi Majiid

thank you very much

## Patrick Gabriel

This was supper helpful

## Patrick Gabriel

This was super helpful

## Timothy1982

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## Nabeela Al-Katheeri

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## Mohammed Kassem

he looks like john wick

## Mutantxslasher Fiogyo

i really like ur intro like if u agree :}

## dani olora

I

## Jagadeesh Ballal

I have a doubt please clear this when 3x is pulled from both means dividing 3x from both the terms how it is divided please tell me the answer

## Jagadeesh Ballal

In inverse distributive property

## yams Yamuta

Thanks for this π

## Allison Sierra Sierra

Thank you I finally understood properties

## Shihab Uddin Tareq

Simple but effective explanation