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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

(−√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.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

JEE

NEET

Foundation JEE

Foundation NEET

CBSE