Question

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

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

The given equation is:

$2x^2+y^2+8z^2-2\sqrt{2}xy+4\sqrt{2}yz-8xz$

=$(\sqrt{2})^{2}x^2+y^2+(2\sqrt{2})^{2}z^2-2\sqrt{2}xy+4\sqrt{2}yz-8xz$

=$(-\sqrt{2}x)^{2}+y^2+(2\sqrt{2}z)^{2}+2(-\sqrt{2}x)y+2y(2\sqrt{2}z)+2(2\sqrt{2}z)(-\sqrt{2}x)$

=$(-\sqrt{2}x+y+2\sqrt{2}z)^{2}$

which is the required answer.