Solve (-a^3-1/2)^2

$$( - a ^ { 3 } - \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{\left(2a^{3}+1\right)^{2}}{4}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(-a^{3}-\frac{1}{2}\right)^{2}.

$$\left(-a^{3}\right)^{2}-\left(-a^{3}\right)+\frac{1}{4}$$

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

$$\left(a^{3}\right)^{2}-\left(-a^{3}\right)+\frac{1}{4}$$

Multiply -1 and -1 to get 1.

$$\left(a^{3}\right)^{2}+a^{3}+\frac{1}{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$a^{6}+a^{3}+\frac{1}{4}$$

Expand

$$a^{6}+a^{3}+\frac{1}{4}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(-a^{3}-\frac{1}{2}\right)^{2}.

$$\left(-a^{3}\right)^{2}-\left(-a^{3}\right)+\frac{1}{4}$$

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

$$\left(a^{3}\right)^{2}-\left(-a^{3}\right)+\frac{1}{4}$$

Multiply -1 and -1 to get 1.

$$\left(a^{3}\right)^{2}+a^{3}+\frac{1}{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$a^{6}+a^{3}+\frac{1}{4}$$