Factor Transition Issue

Question

$$ F'(x)=(2ax+b)e^x+(ax^2+bx+c)e^x=(ax^2+(b+2a)x+c+b)e^x $$

Can someone explain this? I can't understand the transition. What method is this?

Answer 1

$(2ax+b)e^x+(ax^2+bx+c)e^x$ $=2axe^x+be^x+ax^2e^x+bxe^x+ce^x$ $=ax^2e^x+bxe^x+2axe^x+ce^x+be^x$ $=(ax^2+bx+2ax+ce+b)e^x$ $=(ax^2+(b+2a)x+c+b)e^x$