How can a Greatest Common Factor be separated from an expression?

Question

anonymous · Answer

For example take for instance...    6x+3y=15

The highest common factor of (6x+3y) is 3...
So we can take that out to make it look simpler....
Now it is.... 3(2x+y)=15

anonymous · Answer

Or maybe... $$4x ^{3}+8x ^{2}-4x=0$$

Since 4x is in all of the terms we can take it outside of a bracket, this doesn't change the value because if you then expanded the bracket it would go back to the original equation... So this one would be...
$$4x(x ^{2}+2x-1)=0$$ 

This may not look that helpful now, but it becomes incredibly useful for example with fractions as it would allow us to simplify them...For example...
$$\frac{ 4x ^{3} +8x ^{2} -4x}{ x ^{2}+2x-1 }=0$$
Looks complicated right? But lets take out common factors and see how it goes...

$$\frac{ 4x(x ^{2}+2x-1) }{ (x ^{2}+2x-1)}=0$$

See how the two terms can now cancel eachother out (as any number divided by itself is 1)
Now the fraction is simply...

$$4x=0$$

I hope this helped.