1.

Factorise 2x square + Y square + 8 z square - 2√2 xy + 4√2 Y Z - 8 x z

Answer»

This can be written in the FORM of

(-√2x)^2 + (y)^2 + (2√2z)^2 + 2(-√2)(1)xy + 2(1)(2√2)yz + 2(2√2)(-√2)xz

This is in the form of a^2+b^2+c^2 +2ab + 2bc + 2ca which is EQUAL to (a+b+c)^2

Here a= -√2x b=y c=2√2

So it is simplified as

Ans. (-√2x+y+2√2z)^2


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