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 !
