Solve (a^2-1)^2+4a^2

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

Evaluate

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

Solution Steps

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

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

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

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

Combine -2a^{2} and 4a^{2} to get 2a^{2}.

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

Expand

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

Solution Steps

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

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

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

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

Combine -2a^{2} and 4a^{2} to get 2a^{2}.

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