Solve a^{2}-4(a^2-pia^4/4)+4(a^2-25sqrt{3}+pia^2/6)

$$a ^ { 2 } - 4 ( a ^ { 2 } - \frac { \pi a ^ { 4 } } { 4 } ) + 4 ( a ^ { 2 } - 25 \sqrt { 3 } + \frac { \pi a ^ { 2 } } { 6 } )$$

Factor

$$\frac{3\pi a^{4}+2\pi a^{2}+3a^{2}-300\sqrt{3}}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{3a^{2}-3\left(4a^{2}-\pi a^{4}\right)+2\left(6a^{2}-150\sqrt{3}+\pi a^{2}\right)}{3}$$

Evaluate

$$\pi a^{4}+\frac{2\pi a^{2}}{3}+a^{2}-100\sqrt{3}$$