Solve (2b^2-4)^2

$$( 2 b ^ { 2 } - 4 ) ^ { 2 }$$

Evaluate

$$4\left(b^{2}-2\right)^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2b^{2}-4\right)^{2}.

$$4\left(b^{2}\right)^{2}-16b^{2}+16$$

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

$$4b^{4}-16b^{2}+16$$

Expand

$$4b^{4}-16b^{2}+16$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2b^{2}-4\right)^{2}.

$$4\left(b^{2}\right)^{2}-16b^{2}+16$$

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

$$4b^{4}-16b^{2}+16$$