((a^3+125)(a^2-25))/ a^2- 5a+ 25 / ( (a+5)/2)+ 50
You asked:
Evaluate the expression: \(\frac{\left({a}^{3} + 125\right) \cdot \left({a}^{2} - 25\right)}{{a}^{2}} - 5 a + \frac{25}{\frac{a + 5}{2}} + 50\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{\left({a}^{3} + 125\right) \cdot \left({a}^{2} - 25\right)}{{a}^{2}} - 5 a + \frac{25}{\frac{a + 5}{2}} + 50 = - 5 a + 50 + \frac{25}{\frac{a}{2} + \frac{5}{2}} + \frac{\left(a^{2} - 25\right) \left(a^{3} + 125\right)}{a^{2}} \)
Expanded
\[\frac{\left({a}^{3} + 125\right) \cdot \left({a}^{2} - 25\right)}{{a}^{2}} - 5 a + \frac{25}{\frac{a + 5}{2}} + 50 = a^{3} - 30 a + 175 + \frac{25}{\frac{a}{2} + \frac{5}{2}} - \frac{3125}{a^{2}}\]
Factored
\[\frac{\left({a}^{3} + 125\right) \cdot \left({a}^{2} - 25\right)}{{a}^{2}} - 5 a + \frac{25}{\frac{a + 5}{2}} + 50 = \frac{a^{6} + 5 a^{5} - 30 a^{4} + 25 a^{3} + 925 a^{2} - 3125 a - 15625}{a^{2} \left(a + 5\right)}\]