If we start with #y=(x+2)(2x+5)#, and we are trying to convert this into standard form, our first step is to expand this. Later on we'll combine like-terms and tidy up any stray pieces.

So, let's expand #(color(green)(x)+color(orange)(2))*(color(blue)(2x)+color(red)(5))#. #color(green)(x)# multipled by #color(blue)(2x)# is #2x^2# and #color(green)(x)# times #color(red)(5)# equals #5x#. #color(orange)(2)# times #color(blue)(2x)# is #4x#, and #color(orange)(2)# by #color(red)(5)# is #10#. That means we now have #2x^2+5x+4x+10#.

From there we just need to combine like-terms. #5x+4x# is #9x#. That's all we can combine. Let's take another look at the equation: #y=2x^2+9x+10#. That looks like it is in #ax^2+bx+c# format to me, don't 'ya think ;). I think our work is done. Nice job!