How to factorize this polynomial
08-23-2022, 12:02 PM
Post: #1
 rancom Junior Member Posts: 4 Joined: Aug 2022
How to factorize this polynomial
Hi all, I am learning math and learning how to use the HP Prime as well.

How do I factorize 4x^2+36xy+81y^2 and get (2x+9y)^2 as a result?

Things I've tried in CAS view:
- factor(4x^2+36xy+81y^2) -> 36xy+4x^2+81y^2
- factors(4x^2+36xy+81y^2) -> [4*x^2+81*y^2+36*xy,1]
- simplify(4x^2+36xy+81y^2) -> 4x^2+36xy+81y^2
- collect(4x^2+36xy+81y^2) -> 4x^2+81y^2+36xy
- cfactor(4x^2+36xy+81y^2) -> 4x^2+81y^2+36xy
08-23-2022, 05:16 PM
Post: #2
 robmio Member Posts: 170 Joined: Jan 2020
RE: How to factorize this polynomial
(08-23-2022 12:02 PM)rancom Wrote:  Hi all, I am learning math and learning how to use the HP Prime as well.

How do I factorize 4x^2+36xy+81y^2 and get (2x+9y)^2 as a result?

Things I've tried in CAS view:
- factor(4x^2+36xy+81y^2) -> 36xy+4x^2+81y^2
- factors(4x^2+36xy+81y^2) -> [4*x^2+81*y^2+36*xy,1]
- simplify(4x^2+36xy+81y^2) -> 4x^2+36xy+81y^2
- collect(4x^2+36xy+81y^2) -> 4x^2+81y^2+36xy
- cfactor(4x^2+36xy+81y^2) -> 4x^2+81y^2+36xy

You have to put the multiplication sign between the numbers, the variable "x" and the variable "y".
08-23-2022, 05:16 PM
Post: #3
 parisse Senior Member Posts: 1,313 Joined: Dec 2013
RE: How to factorize this polynomial
Add a * between x and y, otherwise xy is interpreted as a single variable with a name identifier of length 2.
08-23-2022, 05:17 PM
Post: #4
 robmio Member Posts: 170 Joined: Jan 2020
RE: How to factorize this polynomial
(08-23-2022 05:16 PM)robmio Wrote:  [quote='rancom' pid='163314' dateline='1661256139']
Hi all, I am learning math and learning how to use the HP Prime as well.

How do I factorize 4x^2+36xy+81y^2 and get (2x+9y)^2 as a result?

Things I've tried in CAS view:
- factor(4x^2+36xy+81y^2) -> 36xy+4x^2+81y^2
- factors(4x^2+36xy+81y^2) -> [4*x^2+81*y^2+36*xy,1]
- simplify(4x^2+36xy+81y^2) -> 4x^2+36xy+81y^2
- collect(4x^2+36xy+81y^2) -> 4x^2+81y^2+36xy
- cfactor(4x^2+36xy+81y^2) -> 4x^2+81y^2+36xy

You have to put the multiplication sign between the numbers, the variable "x" and the variable "y".

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08-23-2022, 05:30 PM (This post was last modified: 08-23-2022 05:31 PM by Steve Simpkin.)
Post: #5
 Steve Simpkin Senior Member Posts: 1,190 Joined: Dec 2013
RE: How to factorize this polynomial
(08-23-2022 05:16 PM)robmio Wrote:
(08-23-2022 12:02 PM)rancom Wrote:  Hi all, I am learning math and learning how to use the HP Prime as well.

How do I factorize 4x^2+36xy+81y^2 and get (2x+9y)^2 as a result?

Things I've tried in CAS view:
- factor(4x^2+36xy+81y^2) -> 36xy+4x^2+81y^2
- factors(4x^2+36xy+81y^2) -> [4*x^2+81*y^2+36*xy,1]
- simplify(4x^2+36xy+81y^2) -> 4x^2+36xy+81y^2
- collect(4x^2+36xy+81y^2) -> 4x^2+81y^2+36xy
- cfactor(4x^2+36xy+81y^2) -> 4x^2+81y^2+36xy

You have to put the multiplication sign between the numbers, the variable "x" and the variable "y".

I don't believe you have to put a multiplication symbol between a number and its variable when entering the equation. For example entering; factor(4x^2+36x*y+81y^2) appears to be automatically interpreted as factor(4*x^2+36x*y+81*y^2) without having to enter the * after the 4, 36 or 81.

08-23-2022, 05:35 PM
Post: #6
 robmio Member Posts: 170 Joined: Jan 2020
RE: How to factorize this polynomial
(08-23-2022 05:30 PM)Steve Simpkin Wrote:
(08-23-2022 05:16 PM)robmio Wrote:  You have to put the multiplication sign between the numbers, the variable "x" and the variable "y".

I don't believe you have to put a multiplication symbol between a number and its variable when entering the equation. For example entering; factor(4x^2+36x*y+81y^2) appears to be automatically interpreted as factor(4*x^2+36x*y+81*y^2) without having to enter the * after the 4, 36 or 81.

Wow, I didn't know. Thank you so much for letting me know this possibility.
Regards, Roberto
08-23-2022, 05:48 PM
Post: #7
 rprosperi Super Moderator Posts: 6,320 Joined: Dec 2013
RE: How to factorize this polynomial
It's beginning to look like Facebook here fellas, 1 or 2 of the same answers are probably enough... LOL

--Bob Prosperi
08-23-2022, 10:35 PM
Post: #8
 toml_12953 Senior Member Posts: 2,113 Joined: Dec 2013
RE: How to factorize this polynomial
(08-23-2022 05:48 PM)rprosperi Wrote:  It's beginning to look like Facebook here fellas, 1 or 2 of the same answers are probably enough... LOL

I know that answers don't show up immediately for me so sometimes I answer a question that's been answered two or three times (or more!) before I see them.

Tom L
Cui bono?
08-24-2022, 07:48 AM
Post: #9
 rancom Junior Member Posts: 4 Joined: Aug 2022
RE: How to factorize this polynomial
(08-23-2022 05:48 PM)rprosperi Wrote:  It's beginning to look like Facebook here fellas, 1 or 2 of the same answers are probably enough... LOL

I found out the answer guys, I have to add a multiplication sign between x and y.

In all seriousness, thank you all for this info!
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