# Factorise please

#### ryanuser

Factorise this expression:
12x to power of 2 minus 27x to power of 2.

I have tried to factorise this using two brackets but I could't work it out.
For example:
(3x-4y)(4x+8y) or (2x-4y)(6x+7y) will not work because there is no third number in the expression.
There as I think this should be alright:
3(4x to power of two - 9y to power of two)
Am I right?

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#### SteamKing

Staff Emeritus
Science Advisor
Homework Helper
You have, I think, (12x)^2 - (27x)^2

When you factor out a constant from this expression, the constant must be squared.

is 12^2 = 3*4^2?
or is 12^2 = 3^2*4*^2?

#### Ray Vickson

Science Advisor
Homework Helper
Dearly Missed
Factorise this expression:
12x to power of 2 minus 27x to power of 2.

I have tried to factorise this using two brackets but I could't work it out.
For example:
(3x-4y)(4x+8y) or (2x-4y)(6x+7y) will not work because there is no third number in the expression.
There as I think this should be alright:
3(4x to power of two - 9y to power of two)
Am I right?
You wrote that you want to factorize $(12x)^2 - (27x)^2.$ Is that what you really want, or did you mean $12 x^2 - 27 x^2$? You can write these out in text as (12x)^2 - (27x)^2 in the first case and as 12 x^2 - 27 x^2 in the second case. No need to write out ""to power of 2"---just use ^, or use the X2 button on the input pallette; it gives you (12x)2 - (27x)2, for example.

#### ryanuser

I have 12x^2-27x^2
Now what?

#### Mark44

Mentor
Factorise this expression:
12x to power of 2 minus 27x to power of 2.

I have tried to factorise this using two brackets but I could't work it out.
For example:
(3x-4y)(4x+8y) or (2x-4y)(6x+7y) will not work because there is no third number in the expression.
There as I think this should be alright:
3(4x to power of two - 9y to power of two)
Am I right?
Is there some reason you didn't use the homework template?

#### ryanuser

What do you mean by homework template?

#### Mark44

Mentor
When you started the thread, didn't you see a template with three parts (problem description, relevant equations, your efforts)? If you are using PF on a phone, the template might not appear.

#### ryanuser

I am in fact using my phone, I have done what you said, I still have no idea of the template, and still not getting the answer yet!!!!!

#### Mark44

Mentor
I have 12x^2-27x^2
Now what?
What factors do 12x2 and -27x2 have in common (i.e., that both have)?

#### ryanuser

They both 3 in common
3x9=27
3x4=12

#### Mark44

Mentor
They both have something else in common.

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