Factorise 12x^2-27x^2: 3(4x^2-9x^2)

[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?

 

[SteamKing]

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]

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]

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]

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]

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

 

[ryanuser]

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

They both have 3 in common

 

[Mark44]

They both have something else in common.