Recall : In a multiplication, the order of the factors does not matter.
Then,
With numbers : 3*4 = 4*3 = 12
With letters : a*b = b * a
We can re-write your expression :
2ab+color(red)(ba)+3b = 2ab + color(red)(ab) + 3b
Now forget for a moment the last term : 3b
->It remains : 2ab + ab, it's 2 times the product of a and b added to the product of a and b.
=>This is the same result that if I multiply directly 3 times the product of ab
We can write : color(blue)(2ab + ab = 3ab)
Consequently our expression is now equal to :
color(blue)(2ab + ab) + 3b = color(blue)(3ab) + 3b
Last step : factorize 3ab + 3b !
After that, we have to find the common factor inside the addition :
3ab=color(red)(3)*a*color(green)(b) and 3b=color(red)(3)*color(green)(b)
Then the common factor of 3ab and 3b is color(red)(3)*color(green)(b)=3b and so : 3ab=3b*a and 3b=3b*1 ( don't forget the 1-factor)
Therefore, the factorization of 3ab + 3b is :
color(blue)(3b)⋅color(red)a color(green)+ color(blue)(3b)⋅color(red)1 = color(blue)(3b).(color(red)a color(green)+ color(red)1)
And it's done, you have your simplified expression ! :)
You can profit of the factorized form to find roots !
