Solve (-1/4x^3-4)^2

$$( - \frac { 1 } { 4 } x ^ { 3 } - 4 ) ^ { 2 }$$

Evaluate

$$\frac{\left(x^{3}+16\right)^{2}}{16}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-\frac{1}{4}x^{3}-4\right)^{2}.

$$\frac{1}{16}\left(x^{3}\right)^{2}+2x^{3}+16$$

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

$$\frac{1}{16}x^{6}+2x^{3}+16$$

Expand

$$\frac{x^{6}}{16}+2x^{3}+16$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-\frac{1}{4}x^{3}-4\right)^{2}.

$$\frac{1}{16}\left(x^{3}\right)^{2}+2x^{3}+16$$

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

$$\frac{1}{16}x^{6}+2x^{3}+16$$