Solve (2a^2-3)^2-8

$$( 2 a ^ { 2 } - 3 ) ^ { 2 } - 8$$

Expand

$$4a^{4}-12a^{2}+1$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a^{2}-3\right)^{2}.

$$4\left(a^{2}\right)^{2}-12a^{2}+9-8$$

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

$$4a^{4}-12a^{2}+9-8$$

Subtract 8 from 9 to get 1.

$$4a^{4}-12a^{2}+1$$

Evaluate

$$\left(2a^{2}-3\right)^{2}-8$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a^{2}-3\right)^{2}.

$$4\left(a^{2}\right)^{2}-12a^{2}+9-8$$

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

$$4a^{4}-12a^{2}+9-8$$

Subtract 8 from 9 to get 1.

$$4a^{4}-12a^{2}+1$$