Y = $(x y + y z)^{2} - 2 x^{2} y^{2} z$
When $x = - 1, y = 1$ and $z = 2$ , |Y| = ___

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Solution

The correct option is B
3

Y = ${(x y + y z)}^{2}$ 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
|Y| = |-3| = 3

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