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

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The expression 12x^2 - 27x^2 can be factored by first identifying the common factor, which is 3. This leads to the expression being rewritten as 3(4x^2 - 9x^2). The discussion highlights confusion over whether to treat the terms as squares, with some participants mistakenly interpreting the expression as (12x)^2 - (27x)^2 instead of 12x^2 - 27x^2. The importance of using the correct format for mathematical expressions is emphasized, as well as the need for clarity in problem-solving. Ultimately, the correct factorization is established as 3(4x^2 - 9x^2).
ryanuser
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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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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?
 
ryanuser said:
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.
 
I have 12x^2-27x^2
Now what?
 
ryanuser said:
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?
 
What do you mean by homework template?
 
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.
 
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!
 
ryanuser said:
I have 12x^2-27x^2
Now what?
What factors do 12x2 and -27x2 have in common (i.e., that both have)?
 
  • #10
They both 3 in common
3x9=27
3x4=12
 
  • #11
ryanuser said:
They both 3 in common
3x9=27
3x4=12

They both have 3 in common
 
  • #12
They both have something else in common.
 

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