(x+y)^3+(X-Y)^3

asked by guest
on Nov 15, 2024 at 7:48 pm



You asked:

Evaluate the expression: \({\left( x + y \right)}^{3} + {\left( X - Y \right)}^{3}\)

MathBot Answer:

Evaluated



\(\displaystyle {\left( x + y \right)}^{3} + {\left( X - Y \right)}^{3} = \left(X - Y\right)^{3} + \left(x + y\right)^{3} \)

Expanded

\[{\left( x + y \right)}^{3} + {\left( X - Y \right)}^{3} = X^{3} - 3 X^{2} Y + 3 Y^{2} X - Y^{3} + x^{3} + 3 x^{2} y + 3 y^{2} x + y^{3}\]

Factored

\[{\left( x + y \right)}^{3} + {\left( X - Y \right)}^{3} = \left(X - Y + x + y\right) \left(X^{2} - 2 X Y - X x - X y + Y^{2} + Y x + Y y + x^{2} + 2 x y + y^{2}\right)\]

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