Revisiting Algebra Basics: 4ax + 2ay = 2a(2x + y)

[Auto Engineer]

Hi All, this is not homework, just some basic revision for my own personal understanding, it's a long time since I went to school?

I would like to refresh my mind on the following algebra please.

4ax + 2ay = 2a x 2x + 2a x y
= 2a(2x + y)

Sorry for not using the DOT product as it does not seem to be available, so had to use X for multiplication?

My misunderstanding of the above is, what happened to the 2a on the right hand side of the first line above?

I understand that 4ax is made up of 2a x 2x = 4ax, and I understand that 2a(2x is made up of the 4ax, but i can't get my head round where the 2a went on the right hand side?

any help greatly appreciated

David

 

[Office_Shredder]

Let's review

4ax+2ay this is your starting equation

2a*2x + 2a*y this is the same equation, only we've split 4ax into 2a*2x and 2ay into 2a*y

2a*(2x+y) you've factored 2a out of the equation. Recall distribution: b*(c+d) = b*c + b*d always. This works backwards just as well...b*c+b*d = b*(c+d) which is what's been done here with b=2a, c=2x, d=y

So what's the sticky point?

 

[Auto Engineer]

Let's review

4ax+2ay this is your starting equation

2a*2x + 2a*y this is the same equation, only we've split 4ax into 2a*2x and 2ay into 2a*y

2a*(2x+y) you've factored 2a out of the equation. Recall distribution: b*(c+d) = b*c + b*d always. This works backwards just as well...b*c+b*d = b*(c+d) which is what's been done here with b=2a, c=2x, d=y

So what's the sticky point?

Hi Office_Shredder. Please stick with the original equation as the "learner" that's "me" is trying to achieve the understanding of the idea of "Factorisation" from first principles, therefore if you expand with more ideas before I gain the basics, I will be lost

Let's start with my original equation;

4ax + 2ay = 2a * 2x + 2a * y (the astrict in my example means multiplication)
=2a(2x + y) (if I now multiply this out I get)
= 4ax +2ay
Here is my problem

2a * 2x = 4ax 2a * y = 2ay, but where did the "other" 2a appear from?

am I right in thinking that the 2a on the left hand side of the equation has been moved to the right hand side, and the y placed inside the bracket?
When I multiply them out the original equation can be found, which seems right, but my understanding is that "if a number on the left hand side of the equals is positive, then moving it to the right hand side should make it negative"?

So; 4ax = 2a * 2x and 2ay = - 2a * y or is there different rules for different types of maths?

David