Solve left(-2x^2+1right)^2

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

Evaluate

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

Solution Steps

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

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

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

$$4x^{4}-4x^{2}+1$$

Expand

$$4x^{4}-4x^{2}+1$$

Solution Steps

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

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

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

$$4x^{4}-4x^{2}+1$$