Subtract $x^{3} - y^{3} + 2 f r o m x^{3} + y^{3} + 3 x y + 1$ using horizontal method.

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Solution

Given that: Subtract $x^{3} - y^{3} + 2 f r o m x^{3} + y^{3} + 3 x y + 1$ using the horizontal method.
Subtracting $x^{3} - y^{3} + 2 f r o m x^{3} + y^{3} + 3 x y + 1$ :
$= x^{3} + y^{3} + 3 x y + 1 - (x^{3} - y^{3} + 2)$
$= x^{3} + y^{3} + 3 x y + 1 - x^{3} + y^{3} - 2 = x^{3} - x^{3} + y^{3} + y^{3} + 3 x y + 1 - 2 = 0 + 2 y^{3} + 3 x y - 1$
$=$ $2 y^{3} + 3 x y - 1$
Therefore, we get $2 y^{3} + 3 x y - 1$

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