Simplify: 7x^3yz + xy(5y + x^2z – z^3) – xy^2 + y^2(2x – z^3+ 3x^2)

asked by guest
on Dec 08, 2024 at 1:21 am



You asked:

Simplify the expression: \(7 {x}^{3} y z + x y \left(5 y + {x}^{2} z - {z}^{3}\right) - x {y}^{2} + {y}^{2} \left(2 x - {z}^{3} + 3 {x}^{2}\right)\)

MathBot Answer:

Simplified:

\[ 7 {x}^{3} y z + x \cdot y\left( 5 y + {x}^{2} z - {z}^{3} \right) - x {y}^{2} + {y}^{2} \left(2 x - {z}^{3} + 3 {x}^{2}\right) = y \left(8 x^{3} z + 3 x^{2} y + 6 x y - z^{3} x - z^{3} y\right) \]


Expanded:

\[ 7 {x}^{3} y z + x \cdot y\left( 5 y + {x}^{2} z - {z}^{3} \right) - x {y}^{2} + {y}^{2} \left(2 x - {z}^{3} + 3 {x}^{2}\right) = 8 x^{3} y z + 3 x^{2} y^{2} + 6 y^{2} x - z^{3} x y - y^{2} z^{3} \]


Factored:

\[ 7 {x}^{3} y z + x \cdot y\left( 5 y + {x}^{2} z - {z}^{3} \right) - x {y}^{2} + {y}^{2} \left(2 x - {z}^{3} + 3 {x}^{2}\right) = y \left(8 x^{3} z + 3 x^{2} y + 6 x y - z^{3} x - z^{3} y\right) \]