Solve (3a^2-1)^2

$$( 3 a ^ { 2 } - 1 ) ^ { 2 }$$

Expand

$$9a^{4}-6a^{2}+1$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a^{2}-1\right)^{2}.

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

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

$$9a^{4}-6a^{2}+1$$

Evaluate

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

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a^{2}-1\right)^{2}.

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

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

$$9a^{4}-6a^{2}+1$$