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Addition and Subtraction of Algebraic Expression

What should b...

Question

What should be added to $2 x y + 3 y z + 4 z x + 5 x y z$ to get $x + y + z + 2 x y + 3 y z + 4 z x - x y z$ ?

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Solution

$\begin{matrix} x + y + z + 2 x y + 3 z y + 4 z x - x y z - (2 x y + 3 y z + 4 z x + 5 x y z) = x + y + z - 6 x y z \end{matrix}$
should be added

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x y - 3 y z + 4 z x

4 x y - 3 z x + 4 y z + 7

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5 x^{2} + 2 x y + y^{2}

3 x^{2} + 4 x y

x^{2} + y^{2} - z^{2} = 21

3 x z + 3 y z - 2 x y = 18

x + y - z = 5

(2 x - y + 3 z) (4 x^{2} + y^{2} + 9 z^{2} + 2 x y + 3 y z - 6 x z)

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