State True or False- 2x2-y2-8z2-2-2xy-4-2yz-8zx - -2x-y-2-2z-2x-y-2-2z

The correct option is A True 2x^2+y^2+8z^2 2√(2)xy+4√(2)yz 8zx=( √(2)x)^2+(y)^2+(2√(2)z)^2+2( √(2)x)(y)+2(y)(2√(2)z)+2(2√(2)z)( √(2)x) ={( √(2)x)+y+2√ ...

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Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

State True or...

Question

State True or False.
$2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 z x$ $= (- \sqrt{2} x + y + 2 \sqrt{2} z) (- \sqrt{2} x + y + 2 \sqrt{2} z)$

True

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False

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Solution

The correct option is A True
$2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 z x = (- \sqrt{2} x)^{2} + (y)^{2} + (2 \sqrt{2} z)^{2} + 2 (- \sqrt{2} x) (y) + 2 (y) (2 \sqrt{2} z) + 2 (2 \sqrt{2} z) (- \sqrt{2} x)$
$= {(- \sqrt{2} x) + y + 2 \sqrt{2} z}^{2} = (- \sqrt{2} x + y + 2 \sqrt{2} z)^{2}$
$= (- \sqrt{2} x + y + 2 \sqrt{2} z) (- \sqrt{2} x + y + 2 \sqrt{2} z)$

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Similar questions

Q. Evaluate:

2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 z x

Q. State True or False.

(- 2 x + 3 y + 2 z)^{2}

= 4 x^{2} + 9 y^{2} + 4 z^{2} - 12 x y + 12 y z - 8 z x

Q. Factorise:

2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 x z

Q. Factorise:

2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 x z

[3 MARKS]

Factorise $2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 x z$

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State True or False.2x2+y2+8z2−2√2xy+4√2yz−8zx = (−√2x+y+2√2z)(−√2x+y+2√2z)

The correct option is A True2x2+y2+8z2−2√2xy+4√2yz−8zx=(−√2x)2+(y)2+(2√2z)2+2(−√2x)(y)+2(y)(2√2z)+2(2√2z)(−√2x)={(−√2x)+y+2√2z}2=(−√2x+y+2√2z)2=(−√2x+y+2√2z)(−√2x+y+2√2z)

State True or False.
$2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 z x$ $= (- \sqrt{2} x + y + 2 \sqrt{2} z) (- \sqrt{2} x + y + 2 \sqrt{2} z)$