5.(i)  Factorise:

   (i)    4x^2 +9y^2 +16z^2 + 12xy -24yz - 16xz

Answers (1)

We can rewrite  4x^2 +9y^2 +16z^2 + 12xy -24yz - 16xz  as

\Rightarrow 4x^2 +9y^2 +16z^2 + 12xy -24yz - 16xz = (2x)^2+(3y)^2+(-4z)^2+2.2x.3y+2.3y.(-4z)+2.(-4z).2x

We will Use identity  

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

Here, a = 2x , b = 3y \ \ and \ \ c = -4z

Therefore,  

4x^2 +9y^2 +16z^2 + 12xy -24yz - 16xz = (2x+3y-4z)^2
 
                                                                                      = (2x+3y-4z)(2x+3y-4z)
 

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