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

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

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

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