# How to read (x - y) ^ 2

I don't know how to read this expression:

(x-y)2 — sometimes rendered in computer code or plain text as (x-y)^2

According to this answer: How to read x^y

I should read that: `x minus y to the power of two` But I'm not sure it's the way that native people read it; And I don't know how to mention parentheses.

• I would use the quantity of..., otherwise it sounds like only y is squared. – Cascabel Feb 6 at 14:12
• @Cascabel I don't know what that mean and I think it still doesn't convey parantheses. – K47 Feb 6 at 14:12
• "The quantity of x minus y, squared." quantity of implies parentheses. – Cascabel Feb 6 at 14:14
• You can say ex minus wye, squared. This one is prone to be confused with x-y^2. You can say the square of ex minus wye. Even though there is no pause in this one for some reason people don't confuse it as much with x^2-y. It seems that people expect a longer pause before minus when calling x^2-y as the square of ex, minus wye. – mama Feb 6 at 17:13
• Another way to say it is to say what is in parentheses, then add "quantity squared". The fact is that any real mathematics has to be worked with in writing. Mathematics is not intended to be pronounced for the most part, and these rules only work for simple expressions like this. Imagine how one might pronounce Maxwell's equations, for instance. – John Lawler Feb 6 at 17:16

## 4 Answers

"The quantity x minus y, all squared."

Commenters have suggested using "quantity" to indicate that x-y is a single expression. I suggest saying "all squared" as a reminder of that.

(Source: mathematician and educator who says/hears this often.)

Edit: I'll add some more thoughts to make this answer more complete and simultaneously address a few comments.

Ultimately, there is not one conventionally "correct" way of reading such an expression out loud or in one's own mind. The goal here is to convey the concept of taking two numbers, which are called x and y, finding the difference x minus y, and then squaring that result. Indeed, mathematical notation is created to fill that purpose! We use the expression (x-y)^2 to mean exactly that idea I just described in words, and this expression will always be unambiguously interpreted in that way.

So, when someone asks, "How do I read that expression out loud?" or "How do I say that expression in my head when I'm reading it in a book?", they are asking for a way to translate that expression from mathematical language into natural language, and this may introduce ambiguities. In some sense, the "correct" way to write/read this expression is the one that is in mathematical language: (x-y)^2 There is not one officially correct way to translate this into natural language. Rather, the best thing to do is to say/write anything that will be interpreted unambiguously as that expression. I suggested "the quantity x minus y, all squared" because I am confident that 100% of my colleagues and students would read those words in natural language and translate them into (x-y)^2 in mathematical language.

Someone suggested "the quantity of x minus y" instead, and this is not really more or less correct in any way. It is just different. I am also confident that my colleagues and students would interpret that as (x-y), but I also suspect that some of them (like me) would bristle a little at the "of", not because it's wrong but because it just sounds redundant and unnecessary. Although, if I were keeping track of how I say out loud what I suggested, I would probably go, "The quantity [short pause] x minus y [short pause] all squared". I suspect the suggested "of" is analogous to the brief pause I would use when saying this out loud.

But ultimately, I hope this sheds more light on these ideas and why I think my answer is best.

• While we usually require sources, a simple search to your bio reveals that you should be an authority on this. Do not be shy. However, this still seems like a partial answer... – Cascabel Feb 6 at 21:11
• Just to be sure: would you say, “The quantity x minus y”, or was there supposed to be an of in there? – Janus Bahs Jacquet Feb 6 at 21:13
• @JanusBahsJacquet: I would say "The quantity x minus y". If I heard "The quantity OF x minus y", I would interpret it the same way, but it just "sounds funny" for some reason. I suspect others would say the same. – Brendan W. Sullivan Feb 6 at 21:15
• @Cascabel: Thanks :-) I just added some thoughts so this is no longer a partial answer. – Brendan W. Sullivan Feb 7 at 18:18
• Yes, I think that's the most critical point: if spoken aloud, it must avoid the possibility of ambiguity, so that each operation is performed on the correct operand(s). Even lazy cops approach things one operation at a time ;-) – Chappo Feb 7 at 23:24

(x-y)^2 — sometimes rendered in computer code or plain text as (x-y)^2

If I was reading this out loud to somebody I would say

x minus y in brackets squared.

I was taught to read (x - y)^2 as

Ex minus wye quantity squared

when I was studying algebra in high school and continued to hear it read that way by math professors in college. Of course, squared is a special case where the power is 2. In the general case of (x - y)^n I was taught to read that as

Ex minus wye quantity, to the power en

I'm not saying other ways of reading it are wrong, I am saying that in math and engineering classes I took in high school and college, that was the convention that I was taught and other people used.

For much greater detail, see the answers to this question (and the references they link to). In particular, see this paper which explicitly recommends speaking ( a + b ) / ( c + d ) as

a plus b quantity over quantity c plus d

The paper also considers all of these phrases acceptable for x^3:

x to the the third

x to the third power

x to the power 3

x raised to the power 3

x cubed

"(x-y)^2"

I would say x-y (parenthesis) times x-y (parenthesis), since this expression means (x-y) * (x-y). (pronouncing parenthesis is optional!)

Then the terms inside the parenthesis are multiplied term by term. You get: x^2 -xy -xy + y^2 which gives us :

x^2 -2xy + y^2 as the answer!

• There are two reasons why this answer is wrong. Firstly, "x minus y times itself" is actually `x - y*y`, which is not the same. Secondly, `^2` doesn't mean "times itself", even though that is the logical outcome. It means "(raised) to the exponent 2" or "to the power 2". Your solution would be meaningless if the exponent were 3, or n, or (2n+1). – Chappo Feb 7 at 22:57