5.(ii) Factorise:

  (ii)    2x^2 + y^2 +8z^2 - 2\sqrt2 xy + 4\sqrt2 yz - 8xz

Answers (1)

We can rewrite  2x^2 + y^2 +8z^2 - 2\sqrt2 xy + 4\sqrt2 yz - 8xz  as

\Rightarrow 2x^2 + y^2 +8z^2 - 2\sqrt2 xy + 4\sqrt2 yz - 8xz = (-\sqrt2x)^2+(y)^2+(2\sqrt2z)^2+2.(-\sqrt2).y+2.y.2\sqrt2z+2.(-\sqrt2x).2\sqrt2z

We will Use identity  

(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca

Here, a = -\sqrt2x , b = y \ \ and \ \ c = 2\sqrt2z

Therefore,  

2x^2 + y^2 +8z^2 - 2\sqrt2 xy + 4\sqrt2 yz - 8xz=(-\sqrt2x+y+2\sqrt2z)^2
 
                                                                                       =(-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z)
 

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