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

  • Thread starter ryanuser
  • Start date
In summary, factorisation is the process of simplifying a mathematical expression by finding common factors between its terms. To factorise a polynomial expression, one must identify common factors and use algebraic techniques like the distributive property and grouping. For example, to factorise 12x^2-27x^2, the common factor of 3 can be factored out, resulting in 3x^2(4-9). The purpose of factorisation is to simplify complex expressions and aid in solving equations and identifying patterns. While not all polynomial expressions can be factorised, most can be simplified using the appropriate methods.
  • #1
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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  • #2
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?
 
  • #3
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.
 
  • #4
I have 12x^2-27x^2
Now what?
 
  • #5
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?
 
  • #6
What do you mean by homework template?
 
  • #7
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.
 
  • #8
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!
 
  • #9
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.
 

1. What is factorisation?

Factorisation is the process of breaking down a mathematical expression into its simplest form by finding the common factors between its terms.

2. How do you factorise a polynomial expression?

To factorise a polynomial expression, you need to identify any common factors between its terms and use algebraic techniques such as the distributive property and grouping to simplify the expression into its simplest form.

3. How do you factorise 12x^2-27x^2?

First, we need to find the common factor between the two terms, which is 3. Then, we can use the distributive property to factor out 3 from both terms, giving us 3(4x^2-9x^2). Finally, we can factor out the common factor of x^2, giving us the simplified expression of 3x^2(4-9).

4. What is the purpose of factorisation?

Factorisation is useful for simplifying complex mathematical expressions, making them easier to work with and understand. It can also help in solving equations and identifying patterns in mathematical relationships.

5. Can you factorise any polynomial expression?

Not all polynomial expressions can be factorised. Some may have no common factors between their terms or may not have any factors that can be factored out using algebraic techniques. However, most polynomial expressions can be factorised using the appropriate methods.

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