Q. 295.0( 1 Vote )

Factorise
(i) x2 + y2 + 9z2 + 2xy + 6yz + 6xz,  
(ii) x2 + 4y2 + 9z2 – 4xy – 12yz + 6xz

Answer :

(i) x2 + y2 + 9z2 + 2xy + 6yz + 6xz
             = x2+(y)2+(3z)2+ 2(x)(y)+2(y)(3z)+2(x)(3z)  
             = (x + y + 3z)2


(ii) x2 + 4y2 + 9z2 _ 4xy – 12yz + 6xz
                  = x2 + (2y)2 + (3z)2 - 2(x)(2y) - 2(2y)(3z)+ 2(x)(3z)    
                  = x2 + (2y)2 + (3z)2 + 2(x)(-2y) + 2(-2y)(3z) + 2(x)(3z)
                  = (x - 2y + 3z)2

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