Question

Factorise◆◆? 2x^2+y^2+8z^2-2under root 2xy + 4 under root 2yz-8zx ​

Answer 1

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).