Question

Factorize 2^2+^2+8^2-2√2+4√2 −8

Answer 1

Answer:

The given equation is:

2x^2+y^2+8z^2-2\sqrt{2}xy+4\sqrt{2}yz-8xz2x

2

+y

2

+8z

2

−2

2

xy+4

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(

2

)

2

x

2

+y

2

+(2

2

)

2

z

2

−2

2

xy+4

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)(−

2

x)

2

+y

2

+(2

2

z)

2

+2(−

2

x)y+2y(2

2

z)+2(2

2

z)(−

2

x)

=(-\sqrt{2}x+y+2\sqrt{2}z)^{2}(−

2

x+y+2

2

z)

2

which is the required answer.