(48yz+(2y^2(z^2)))/(y+2z)^2

asked by guest
on Apr 04, 2025 at 1:40 pm



You asked:

Evaluate the expression: 48yz+2y2z2(y+2z)2\frac{48 y z + 2 {y}^{2} {z}^{2}}{{\left( y + 2 z \right)}^{2}}

MathBot Answer:

Evaluated



48yz+2y2z2(y+2z)2=2y2z2+48yz(y+2z)2\displaystyle \frac{48 y z + 2 {y}^{2} {z}^{2}}{{\left( y + 2 z \right)}^{2}} = \frac{2 y^{2} z^{2} + 48 y z}{\left(y + 2 z\right)^{2}}

Expanded

48yz+2y2z2(y+2z)2=2y2z2y2+4yz+4z2+48yzy2+4yz+4z2\frac{48 y z + 2 {y}^{2} {z}^{2}}{{\left( y + 2 z \right)}^{2}} = \frac{2 y^{2} z^{2}}{y^{2} + 4 y z + 4 z^{2}} + \frac{48 y z}{y^{2} + 4 y z + 4 z^{2}}

Factored

48yz+2y2z2(y+2z)2=2yz(yz+24)(y+2z)2\frac{48 y z + 2 {y}^{2} {z}^{2}}{{\left( y + 2 z \right)}^{2}} = \frac{2 y z \left(y z + 24\right)}{\left(y + 2 z\right)^{2}}

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