Solve left(2-x^3right)^2

$${ \left(2- { x }^{ 3 } \right) }^{ 2 }$$

Expand

$$x^{6}-4x^{3}+4$$

Solution Steps

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

$$4-4x^{3}+\left(x^{3}\right)^{2}$$

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

$$4-4x^{3}+x^{6}$$

Evaluate

$$\left(2-x^{3}\right)^{2}$$

Solution Steps

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

$$4-4x^{3}+\left(x^{3}\right)^{2}$$

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

$$4-4x^{3}+x^{6}$$