\left(\frac{m^{2}-4}{2m}\right)^{8}

asked by guest
on Mar 14, 2025 at 8:14 am



You asked:

Evaluate the expression: (m2−42m)8{\left( \frac{{m}^{2} - 4}{2 m} \right)}^{8}

MathBot Answer:

Evaluated



(m2−42m)8=(m2−4)8256m8\displaystyle {\left( \frac{{m}^{2} - 4}{2 m} \right)}^{8} = \frac{\left(m^{2} - 4\right)^{8}}{256 m^{8}}

Expanded

(m2−42m)8=m8256−m68+7m44−14m2+70−224m2+448m4−512m6+256m8{\left( \frac{{m}^{2} - 4}{2 m} \right)}^{8} = \frac{m^{8}}{256} - \frac{m^{6}}{8} + \frac{7 m^{4}}{4} - 14 m^{2} + 70 - \frac{224}{m^{2}} + \frac{448}{m^{4}} - \frac{512}{m^{6}} + \frac{256}{m^{8}}

Factored

(m2−42m)8=(m−2)8(m+2)8256m8{\left( \frac{{m}^{2} - 4}{2 m} \right)}^{8} = \frac{\left(m - 2\right)^{8} \left(m + 2\right)^{8}}{256 m^{8}}

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