Simplify the following expression:
$(5 x y + 3 x^{2} - 12 y + 5 x) + (x y - 3 x - 12 y z + 5 x^{3}) + (y - 3 x^{2} - z y - 5 x^{3}) .$

6 x y + 11 y - 2 x + 13 y z

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6 x y + 11 y + 2 x - 13 y z

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6 x y - 11 y + 2 x - 13 y z

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6 x y - 11 y + 2 x + 13 y z

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Solution

The correct option is C $6 x y - 11 y + 2 x - 13 y z$
We have,
$(5 x y + 3 x^{2} - 12 y + 5 x) + (x y - 3 x - 12 y z + 5 x^{3}) + (y - 3 x^{2} - z y - 5 x^{3})$
$= 5 x y + 3 x^{2} - 12 y + 5 x + x y - 3 x - 12 y z + 5 x^{3} + y - 3 x^{2} - z y - 5 x^{3}$ [Solving the parentheses]
$= 5 x y + x y + 3 x^{2} - 3 x^{2} - 12 y + y + 5 x - 3 x - 12 y z - z y + 5 x^{3} - 5 x^{3}$ [Rearranging the like terms]
$= 6 x y - 11 y + 2 x - 13 y z$ [Simplifying]

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Simplify the following expression: (5xy+3x2–12y+5x)+(xy–3x–12yz+5x3)+(y–3x2–zy–5x3).

Simplify the following expression:
$(5 x y + 3 x^{2} - 12 y + 5 x) + (x y - 3 x - 12 y z + 5 x^{3}) + (y - 3 x^{2} - z y - 5 x^{3}) .$