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The factors of the following expression 2x² + y² + 8z² – 2√2xy +4√2yz– 8xz is:

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(−√2x + y + 2√2z) (−2√x + y + √2z)

(−√2x + y + 2√2z) (−2√x + y + 2√2z)

(−√2x + y + 2√2z) (−2√x + y + 3√2z)

(−√2x + y + 2√2z) (−2√x + y + 4√2z)

answer is B.

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Detailed Solution

Given: 2x² + y² + 8z² – 2√2xy + 4√2yz – 8xz
Let us rewrite the given expression as:

= (− 2 x) 2 + (y) 2 + (2 2 z) 2 + (2 × (− 2 x) × y) + (2 × y × 2 2 z) + (2 × 2 2 z × (− 2 x))

Again by using algebraic identity,(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca, we get:

= (− 2 x + y + 2 2 z) 2

= (− 2 x + y + 2 2 z □) (− 2 x + y + 2 2 z)

Hence, the value of the expression is

(− 2 x + y + 2 2 z □) (− 2 x + y + 2 2 z)

.
Therefore, the correct option is 2.

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