       Re: How to collect terms based the total power of x and y

• To: mathgroup at smc.vnet.net
• Subject: [mg92195] Re: [mg92158] How to collect terms based the total power of x and y
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 22 Sep 2008 07:26:08 -0400 (EDT)
• Reply-to: hanlonr at cox.net

```expr = 1 + 3 x + 3 x^2 + x^3 + 3 y + 6 x y + 3 x^2 y + 3 y^2 +
3 x y^2 + y^3

x^3+3 y x^2+3 x^2+3 y^2 x+6 y x+3 x+y^3+3 y^2+3 y+1

List @@ Collect[expr /. {x -> x*z, y -> y*z}, z] /. z -> 1

{1,3 x+3 y,3 x^2+6 y x+3 y^2,x^3+3 y x^2+3 y^2 x+y^3}

expr == Total[%] == Plus @@ %

True

Bob Hanlon

---- Peng Yu <PengYu.UT at gmail.com> wrote:

=============
Hi,

In[(x + y + 1)^3 // Expand

The above command gives me the following results.

1 + 3 x + 3 x^2 + x^3 + 3 y + 6 x y + 3 x^2 y + 3 y^2 + 3 x y^2 + y^3

I'm wondering how to collect terms based on the sum of the power
coefficients of both x and y. For example, I want the following

1 + (3 x + 3 y) + (3 x^2 + 6 x y + 3 y^2) + (x^3 + 3 x^2 y + 3 x y^2 +
y^3)

Thanks,
Peng

--

Bob Hanlon

```

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