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paulb203

Member

Registered: 2023-02-24

Posts: 321

Brackets; like terms; do the brackets always matter?

At the end of the Maths is Fun page on, “Algebra – Basic Definitions” there is a brief explanation of like terms.

One of the terms given in the example is (1/3)xy^2, the other two are, -2xy^2, and, 6xy^2.

What is the significance of the brackets around 1/3?

In this context would there be a difference between (1/3)xy^2, and just, 1/3xy^2?

Also, what would (1/3)xy^2 – 2xy^2 + 6xy^2 equal?

I’m confident that it would at least equal; (1/3)xy^2 + 4xy^2?

But could we go further and get; 4 1/3 xy^2? Or do the brackets prevent us from adding the 1/3 and the 4?

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Brackets; like terms; do the brackets always matter?

hi paulb203

Some people might (incorrectly) think that 1/3xy^2 means

You would definitely need brackets if that was what was meant ... 1/(3xy^2)

Actually that bracket around (1/3) isn't strictly necesary but it doesn't hurt to make the meaning clear ... ie. it's the fraction one third times xy^2.

Your simplification to 4 1/3 xy^2  is correct.  Trouble is someone might interpret that as forty one over three.  That's where Latex comes in handy:

You can look up about order of precedence of operators here

https://www.mathsisfun.com/operation-order-bodmas.html

and about using Latex here:

http://www.mathisfunforum.com/viewtopic.php?id=4397

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

cheetahflycello

Novice

Registered: 2023-04-19

Posts: 6

Re: Brackets; like terms; do the brackets always matter?

The brackets around 1/3 indicate that the fraction applies only to the x and y^2 terms, not to any additional terms that might appear in the expression. If the brackets were not there, it would imply multiplication of the entire expression by 1/3.

In this context, there is no difference between (1/3)xy^2 and 1/3xy^2. The parentheses are optional and only serve to make it clear that the 1/3 applies to the x and y^2 terms.

To simplify (1/3)xy^2 - 2xy^2 + 6xy^2, we combine the like terms (terms with the same variables and exponents).

(1/3)xy^2 - 2xy^2 + 6xy^2 = (1/3)xy^2 + 4xy^2

We cannot add the 1/3 and the 4 because they are not like terms. The expression is already in its simplest form, so we cannot simplify it any further.