Factorizing problem

[Mechaman]

Hi, have a question, not sure where the factorizing came from:

(6x^2)cos2x + (6x)sin2x

= 6x(xcos2x + sin2x)

it looks like 6x was factored out of both but why is there now an x in front of the cos?

 

[stapel]

Hi, have a question, not sure where the factorizing came from:

(6x^2)cos2x + (6x)sin2x

= 6x(xcos2x + sin2x)

it looks like 6x was factored out of both but why is there now an x in front of the cos?

If you factor an x out of x², what is left?

 

[Steven G]

Hi, have a question, not sure where the factorizing came from:

(6x^2)cos2x + (6x)sin2x

= 6x(xcos2x + sin2x)

it looks like 6x was factored out of both but why is there now an x in front of the cos?

I'll take a crack at explaining this. 6x^2 = 6*x*x

(6x^2)cos2x + (6x)sin2x= 6*x*x*cos2x + 6*x*sin2x.

Now what is common in the red AND brown. The answer is 6*x. So we factor out the 6x and leave everything else inside the parenthesis.
So 6*x*x*cos2x+ 6*x*sin2x = 6*x(xcos2x+ sin2x)

 

[Mechaman]

Thanks for the help, understood now!