Solve (5/6-1/16u^8)^2

$$( \frac { 5 } { 6 } - \frac { 1 } { 16 } u ^ { 8 } ) ^ { 2 }$$

Evaluate

$$\frac{\left(40-3u^{8}\right)^{2}}{2304}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{5}{6}-\frac{1}{16}u^{8}\right)^{2}.

$$\frac{25}{36}-\frac{5}{48}u^{8}+\frac{1}{256}\left(u^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{25}{36}-\frac{5}{48}u^{8}+\frac{1}{256}u^{16}$$

Expand

$$\frac{u^{16}}{256}-\frac{5u^{8}}{48}+\frac{25}{36}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{5}{6}-\frac{1}{16}u^{8}\right)^{2}.

$$\frac{25}{36}-\frac{5}{48}u^{8}+\frac{1}{256}\left(u^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{25}{36}-\frac{5}{48}u^{8}+\frac{1}{256}u^{16}$$