Question

2x^2 + y^2 + 8z^2 – 2 √2 xy + 4 √2 yz – 8xz​

Answer 1

Answer:

$The answer is (-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).)Step-by-step explanation: We are given to factorise the following expression:E=2x^2+y^2+8z^2-2\sqrt2xy+4\sqrt 2yz-8xz.We will be using the following factorisation formula:(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca.We haveE\\\\=2x^2+y^2+8z^2-2\sqrt2xy+4\sqrt 2yz-8xz\\\\=(-\sqrt2x)^2+y^2+(2\sqrt2z)^2+2(-\sqrt2x)y+2y(2\sqrt2z)+2(2\sqrt2z)(-\sqrt2x)\\\\=(-\sqrt2x+y+2\sqrt2z)^2\\\\=(-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).$

Answer 2

QUESTION -

Evaluate :- 2x^2 + y^2 + 8z^2 – 2 √2 xy + 4 √2 yz – 8xz

ANSWER -

We can solve this sum using an identity..

(a+b+c)2 = a2 + b2 + c2 + 2ab+2bc+2ca

= (√2x)2 + y2 + (2√2z)2+2√2xy

+ (4√2zy)2 + (2√4xz)2

= (√2x + y + 2√2z)2

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