Question

Factorise 2x^2+y^2+8z^2-2√2xy+4√2yz-8xz

Answer 1

Hope this will help you !

Answer 2

Answer: The answer is $(-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).$)

Step-by-step explanation:  We are given to factorise the following expression:

$E=2x^2+y^2+8z^2-2\sqrt2xy+4\sqrt 2yz-8xz.$

We will be using the following factorisation formula:

$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca.$

We have

$E\\\\=2x^2+y^2+8z^2-2\sqrt2xy+4\sqrt 2yz-8xz\\\\=(-\sqrt2x)^2+y^2+(2\sqrt2z)^2+2(-\sqrt2x)y+2y(2\sqrt2z)+2(2\sqrt2z)(-\sqrt2x)\\\\=(-\sqrt2x+y+2\sqrt2z)^2\\\\=(-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).$

Thus, the answer is $(-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).$