Question

Factorise:
(i) 2x2 + y2 + 8z2 - 2/2 xy + 4/2 yz - 8xz
(ii) x2 +9y2 + 36z^2 + 6xy + 36yz + 12xz.
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Answer 1

Given

1 ) 2x2 + y2 + 8z2 - 2√(2xy) + 4√(2yz) - 8xz

= (-√2x)2 + y2 + {2√(2z)}2 - 2{(-√2x)*y} + 2y*{2√(2z)} + 2*(-√2x)*{2√(2z)}

= {-√2x + y + 2√(2z)}2

= {-√2x + y + 2√(2z)}*{-√2x + y + 2√(2z)}