2 x2-y2-8 z2-2 -2 x y-4 -2 y z-8 x z- How to factorise it-

Answer: Given, 2x2 + y2 + 8z2 2√2xy + 4√2yz – 8xz This expression can be written as follows: ( √2x)2 + y2 + (2√2z) 2 + 2( √2x*z) + 2(y*2√2z) + 2(√2x*2√2z) I ...

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Byju's Answer

Standard IX

Mathematics

Solving Equations Using Method of Substitution

2 x2+y2+8 z2-...

Question

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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Solution

$2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 x z$
$= (\sqrt{2} x)^{2} + (y)^{2} + (2 \sqrt{2} z)^{2} - 2 (\sqrt{2} x) (y) + 2 (2 \sqrt{2} z) (y) - 2 (\sqrt{2} x) (2 \sqrt{2} z)$
Using $a^{2} + b^{2} + c^{2} = 2 a b + 2 b c + 2 a c = (a + b + c)^{2}$ , we get,
$a = \sqrt{2} x$ , $b = y$ and $c = 2 \sqrt{2} z$
$= (\sqrt{2} x + y + 2 \sqrt{2} z)^{2}$

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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

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Q. Question 5
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(i) 4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z (i i) 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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2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 z x

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Factorise 2x2+y2+8z2−2√2xy+4√2yz−8xz

2x2+y2+8z2−2√2xy+4√2yz−8xz=(√2x)2+(y)2+(2√2z)2−2(√2x)(y)+2(2√2z)(y)−2(√2x)(2√2z)Using a2+b2+c2=2ab+2bc+2ac=(a+b+c)2, we get,a=√2x, b=y and c=2√2z=(√2x+y+2√2z)2

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