Newb needs assistance basic: (2y * 3x) + 2 = 7xy??

[Ansego]

Im a newb, so please be patient.

Are these correct?

1: (2y * 3x) + 2 = 7xy??

2: (2y + 3x)+(3y + 2x) = 5y + 5x OR 10xy??

(Note below: I dont know how to do small cube or square symbols sorry)

3: (2y^2 + 3x^3)+(3y^3 + 2x^2) = 5y^5 + 5x^5 OR 10xy^10??

4: (2y^2 + 3x^3)+2(3y^3 + 2x^2)+3 = 7y^5 + 8x^5 OR 15xy^10??

I hope I am on the right track here, I assume it would work simular with times or divide.

Advance thanks.

 

[mmm4444bot]

We use the caret symbol ^ to show exponentiation. I have edited your post.

(2y * 3x) + 2 = 7xy

This is incorrect. 2*3=6

2y*3x + 2

6xy + 2

That's as far as we can go. 6xy is a variable term, and 2 is a constant term. We can only combine like terms, so we're done.

(2y + 3x) + (3y + 2x) = 5y + 5x OR 10xy

5x + 5y is correct! These two terms are unlike each other; we cannot combine them.

(If you ever see the expressions 2x*5y or 5x*2y, they each simplify to 10xy.)

(2y^2 + 3x^3) + (3y^3 + 2x^2) = 5y^5 + 5x^5 OR 10xy^10

Both of these are incorrect. There are no like terms, in the given expression (there's an x^2 term, an x term, a y^2 term and a y term), so none of them can be combined.

You can remove the grouping symbols because they're not doing anything to change the order of operations. You could reorder the terms, if you like, but it's not necessary.

3x^3 + 2x^2 + 3y^3 + 2y^2

(2y^2 + 3x^3) + 2(3y^3 + 2x^2) + 3 = 7y^5 + 8x^5 OR 15xy^10

Both of these are incorrect. You need to see the different types of terms.

(2y^2 + 3x^3) + 2(3y^3 + 2x^2) + 3

3x^3 (x cubed term)
2x^2 (x squared term)
3y^3 (y cubed term)
3y^2 (y squared term)
3 (constant term)

As there are no like terms, we cannot combine any of them.

You can remove the first pair of parentheses; doing so will not change anything. To remove the second set of parentheses, you apply the Distributive Property (i.e., multiply each term inside the parentheses by 2).

After distributing the 2, you are done. What do you get? :cool:

 

[Ansego]

Thanks so much @mmm4444bot

To clarify, if no expression and exponentiation is the same such as x, y, ^2 or ^3 etc, none of these can be combined? hope im on track here, and a constaint varible will always be alone and never combined unless to another constant?

And the grouping was pointless because none of the formula could be combined is this correct?

Would I be correct in saying algebra are just formulars and the math's that is done is just to simplify the formular?

Kind regards

 

[mmm4444bot]

To clarify, if no expression and exponentiation is the same such as x, y, ^2 or ^3 etc, none of these can be combined? … and a [constant] will always be alone and never combined unless to another constant?

That's right. The terms must be like each other, to be combined.

If you google "how to combine like terms", you can find many on-line examples, lessons, and videos.

And the grouping was pointless because none of the formula could be combined is this correct?

I would say that the grouping symbols in exercise (3) are pointless because we can add things in any order we like. (See the Commutative Property of Addition.)

Grouping symbols are used to change the Order of Operations. In cases where the order doesn't matter, grouping symbols are not needed. Consider the following expressions.

4x^2 + 3x + 2x^2 + 5x + 1

3x + 2x^2 + 5x + 1 + 4x^2

4x^2 + (3x + 2x^2) + 5x + 1

(4x^2 + 3x) + 2x^2 + 5x + 1

(4x^2 + 3x) + (2x^2 + 5x + 1)

(5x + 3x) + (2x^2 + 4x^2) + 1

Each of these expressions simplifies to 6x^2 + 8x + 1. The grouping symbols do nothing.

Would I be correct in saying algebra are just formulars and the math's that is done is just to simplify the formular?

I would not use the word "just".

Algebra uses formulas and rules, but algebra is more about symbolic thinking and recognizing patterns. We need the symbols and rules, to be sure that we work with symbolic numbers the same way as actual numbers (i.e., doing the right steps in the right order). Simplifying expressions is part of the mechanics of algebra, but the big picture is using algebra to help us with abstract things in the world.

 

[Deleted member 4993]

Thanks so much @mmm4444bot

To clarify, if no expression and exponentiation is the same such as x, y, ^2 or ^3 etc, none of these can be combined? hope i'm on track here, and a constant variable will always be alone and never combined unless to another constant?

And the grouping was pointless because none of the formula could be combined is this correct?

Would I be correct in saying algebra are just formulas and the math's that is done is just to simplify the formula?

Kind regards

That depends on what you exactly mean by combined!

An expression like:

x^3 + 3x^2*y + 3x*y^2 + y^3 can be written as (x + y)^3

and most of the time that would desired next step.

 

[mmm4444bot]

That depends on what you exactly mean by combined!

I think Ansego used my wording, as I've been posting about combining like-terms (adding/subtracting).

x^3 + 3x^2*y + 3x*y^2 + y^3 can be written as (x + y)^3

Combined? That's deep, man.

 

[Ansego]

A big Thanks @PMmmm4444bot && Subhotosh Khan

I will check those resourses PMmmm4444bot, lots to learn, appreciate your time guys.

Thanks