Simplify $(x y + y z)^{2} - 2 x^{2} y^{2} z$ and find the value when $x = - 1, y = 1$ and $z = 2.$

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-3

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Solution

The correct option is C
-3

Simplify ${(x y + y z)}^{2}$ using the identity ${(a + b)}^{2}$ = $a^{2}$ + $b^{2} + 2 a b$

We get ${(x y + y z)}^{2}$ = $x^{2}$ $y^{2}$ + $y^{2}$ $z^{2}$ + ${2 x z y}^{2}$ .

Therefore,

${(x y + y z)}^{2}$ - $2 x^{2}$ $y^{2} z$ = $x^{2}$ $y^{2}$ + $y^{2}$ $z^{2}$ + $2 x z y^{2}$ - 2 $x^{2}$ $y^{2} z$

Placing the values of x,y and z in the above expression we get,

$1 - 4 - 4 - 4 = - 3$

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Similar questions

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

x = - 1, y = 1

z = 2

Simplify $(x y + y z)^{2} - 2 x^{2} y^{2} z .$
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