Solve left(2a^2-1right)^2

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

Expand

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

Solution Steps

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

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

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

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

Evaluate

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

Solution Steps

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

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

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

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