Rearrangement of Parabola

Question

I am attempting to show that the following expression -

$2 [(P)x^2 + (P+Q)x + P)$

can be rewrriten as $2 (x+1)(Px + Q$)...

but I have come to no help.

I did manage to get to
$Px (x+1) + Q(x+1)$ but I am unsure how I can proceed since I

think I have done something wrong.

How can I prove that the first expression equates to the second?

Thanks.

Answer 1

May be your question is $$\displaystyle 2\left[Px^2+(P+Q)x+Q\right]\;,$$Then

$$Px^2+(P+Q)x+Q = \underbrace{Px^2+Px}+\underbrace{Qx+Q} = Px(x+1)+Q(x+1) = (Px+Q)(x+1)$$

So $$\displaystyle 2\left[Px^2+(P+Q)x+Q\right]=2(Px+Q)(x+1)$$