How to read (x - y) ^ 2 [duplicate]

Question

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.

Answer 1

"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.

Answer 2

(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.

Answer 3

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

Answer 4

"(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!