[SPLIT] factoring 12x^2 - 3

Re: Complex Equations???

These kind of questions usually tell you that it's a difference of squares problem:
\(\displaystyle a^{2} - b^{2} = (a-b)(a+b)\)

First factor out a 3 so that it'll be easier to deal with: \(\displaystyle 3(4x^{2} - 1)\).

So using our difference of squares formula, you get \(\displaystyle a^{2} = 4x^{2}\) and \(\displaystyle b^{2} = 1\). What's a and b? Once you find that, just plug it back into the formula I gave you (a+b)(a-b)
 
Re: Complex Equations???

o_O said:
These kind of questions usually tell you that it's a difference of squares problem:
\(\displaystyle a^{2} - b^{2} = (a-b)(a+b)\)

First factor out a 3 so that it'll be easier to deal with: \(\displaystyle 3(4x^{2} - 1)\).

So using our difference of squares formula, you get \(\displaystyle a^{2} = 4x^{2}\) and \(\displaystyle b^{2} = 1\). What's a and b? Once you find that, just plug it back into the formula I gave you (a+b)(a-b)
Click to expand...

Does a=4x and b=+/-1?
 
Re: Complex Equations???

b = 1 is correct. No need for the \(\displaystyle \pm\) since it's compensated by the two binomial expressions. As for a = 4x, not quite. When you square it, you get a[sup:3ci3ux1i]2[/sup:3ci3ux1i] = 16x[sup:3ci3ux1i]2[/sup:3ci3ux1i] which isn't what you started with. Keep trying ... a[sup:3ci3ux1i]2[/sup:3ci3ux1i] = 4x[sup:3ci3ux1i]2[/sup:3ci3ux1i] ...
 
Re: Complex Equations???

o_O said:
b = 1 is correct. No need for the \(\displaystyle \pm\) since it's compensated by the two binomial expressions. As for a = 4x, not quite. When you square it, you get a[sup:1swrsnb0]2[/sup:1swrsnb0] = 16x[sup:1swrsnb0]2[/sup:1swrsnb0] which isn't what you started with. Keep trying ... a[sup:1swrsnb0]2[/sup:1swrsnb0] = 4x[sup:1swrsnb0]2[/sup:1swrsnb0] ...
Click to expand...

So, b=1 and a=2x?
 
Re: Complex Equations???

Yep, now use your formula to get the factored form of your expression. Don't forget the 3 that you factored out at the beginning!
 
I give up. I cannot figure out how the new script's "merge" tool is supposed to work, so the replies from the other "half" of this conversation have been copied and pasted below. Apologies for any confusion. :oops:

xwintersnight said:
o_O said:
These kind of questions usually tell you that it's a difference of squares problem:
\(\displaystyle a^{2} - b^{2} = (a-b)(a+b)\)

First factor out a 3 so that it'll be easier to deal with: \(\displaystyle 3(4x^{2} - 1)\).

So using our difference of squares formula, you get \(\displaystyle a^{2} = 4x^{2}\) and \(\displaystyle b^{2} = 1\). What's a and b? Once you find that, just plug it back into the formula I gave you (a+b)(a-b)
Click to expand...

So, would it end up being 3(2x+1)(2x-1)?
Click to expand...
 
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