Chapter 4: Equilibrium

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I cannot follow the algebra and some steps taken in this question. Can someone please help?

From the answer:
Pi = Pf
MiVi = MfVf
MA∙VAi + MB∙VBi = MA∙VAf + MB∙VBf
-Got it-
M∙V + 2M x 0 m/s = M∙VAf + 2M x VBf
M∙V = M (VAf + 2VBf)
V = VAf + 2VBf
VAf = V – 2VBf
-Good so far-

"Also, from conservation of kinetic energy:"
-Why do we have to do this step?-
Ek = 1/2 mv2
Ek = 1/2 M∙V2 = 0.5M∙VAf2 + 0.5 x 2M∙VBf2
-is the above basically: 1/2 mv2=1/2 mAv2+1/2 mBv2?
M∙V2 = M∙VAf2 + 2M∙VBf2
V2 = VA2 + 2VB2
VA2 = V2 – 2VB2
-I understand the above algebra, but I don't understand the next step(s)-

"Substituting in conservation of momentum:" -Why and how-
VAf = V – 2VBf
VAf2 = (V - 2VBf)2 -how do we get to this step-
VAf2 = V2 – 4V∙VB + 4VBF
V2 – 2VB2 –4V∙VB + 4VB2 -how do we get here-

I know these are a lot of questions, but I am lost.