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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply a^{2} by a^{2}+1.

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

Use the distributive property to multiply a^{2} by a^{4}+a^{2}-1.

$$a^{2}+1-\left(a^{6}+a^{4}-a^{2}\right)$$

To find the opposite of a^{6}+a^{4}-a^{2}, find the opposite of each term.

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

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

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

Expand

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

Solution Steps

Use the distributive property to multiply a^{2} by a^{2}+1.

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

Use the distributive property to multiply a^{2} by a^{4}+a^{2}-1.

$$a^{2}+1-\left(a^{6}+a^{4}-a^{2}\right)$$

To find the opposite of a^{6}+a^{4}-a^{2}, find the opposite of each term.

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

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

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