If Raju and Kishan filled a box with chocolates, Raju put $x^{2} + 3 x y + 9 x z$ chocolates and Kishan put $x^{3} - 2 x^{2} + 2 y z$ chocolates, their friend Ravi came and took $x^{3} - x^{2} - x y$ chocolates, how many chocolates are remaining in the box?

x^{3} + 4 x y + 9 x z + 2 y z

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2 x^{2} + 4 x y + 9 x z + 2 y z

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4 x y + 9 x z + 2 y z

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4 x y + 9 x z - 2 y z

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Solution

The correct option is C $4 x y + 9 x z + 2 y z$
Total number of chocolates filled by Raju and Kishan in the box:
$(x^{2} + 3 x y + 9 x z) + (x^{3} - 2 x^{2} + 2 y z)$
$= x^{3} + x^{2} - 2 x^{2} + 3 x y + 9 x z + 2 y z$
$= x^{3} - x^{2} + 3 x y + 9 x z + 2 y z$

Number of chocolates remaining in the box:
$(x^{3} - x^{2} + 3 x y + 9 x z + 2 y z) - (x^{3} - x^{2} - x y)$
$= x^{3} - x^{3} - x^{2} + x^{2} + 3 x y + x y + 9 x z + 2 y z$
$= 4 x y + 9 x z + 2 y z$

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Akash has $6 x y + 4 x y^{2}$ chocolates. He wants to distribute them to 2x children. How many chocolates does each of the child get if y = 2?

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