# Math Help - factorising

1. ## factorising

hi this is my question, i need to factorise this:

x^2 - 81?

im having a few problems with factorising at the moment so could someone let me know how to work this out!
would i be correct if i did this (x^2 - 81)??

Thanks

2. No, that's still the original problem.

This question is classic difference of two squares: $a^2-b^2 = (a-b)(a+b)$. To make it more apparent you can write it as $x^2-9^2$

http://en.wikipedia.org/wiki/Difference_of_two_squares

3. so i make it x^2 - 9^2 then do i put them in brackets? if so would i do this, (x -3) (x -3) ??

4. No, that would be the case if it said $x^2-9$

5. would it be (x -9) (x -9)? because 9x9=81?

6. x^2 - 9^2=x^2+9x-9x-9^2=x(x+9)-9(x+9)=(x+9)(x-9)

7. yes...

8. Originally Posted by andyboy179
would it be (x -9) (x -9)? because 9x9=81?
actually no, because 9x9=81 and we need -81 so it would be (x +9) (x -9)!

9. sorry..you are right ..the result is (x +9) (x -9)

10. okay, thankyou very much!

but on this type of factorising question what would i do?

3a+15b-30c?
would it = 3(a+5b+10c)?

11. yes...
3a+15b-30c=3*a+ 3*5b-3*10c=3*(a+5b-10c)

12. really sorry again..your factorisation is not right...why did you change - to +?

13. yes!! lastly how would i work out this:

x^2 - 4x -45?

would i do, (x -45) (x +41) ???

14. oh, how is it not right??

15. Originally Posted by andyboy179
yes!! lastly how would i work out this:

x^2 - 4x -45?

would i do, (x -45) (x +41) ???
I shall be very surprised if $-45 \cdot 41 = 45\!$!

Look for two numbers that are factors of -45 and sum to -4. As a hint 9 and 5 are two such numbers

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