Solve left(1-3x^4right)^2

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

Expand

$$9x^{8}-6x^{4}+1$$

Solution Steps

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

$$1-6x^{4}+9\left(x^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$1-6x^{4}+9x^{8}$$

Evaluate

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

Solution Steps

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

$$1-6x^{4}+9\left(x^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$1-6x^{4}+9x^{8}$$