Solve (x^2+1)(x^2-1)(x^2+1)

$$( x ^ { 2 } + 1 ) ( x ^ { 2 } - 1 ) ( x ^ { 2 } + 1 )$$

Evaluate

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

Solution Steps

Multiply x^{2}+1 and x^{2}+1 to get \left(x^{2}+1\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+1\right)^{2}.

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

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

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

Use the distributive property to multiply x^{4}+2x^{2}+1 by x^{2}-1 and combine like terms.

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

Expand

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

Solution Steps

Multiply x^{2}+1 and x^{2}+1 to get \left(x^{2}+1\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+1\right)^{2}.

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

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

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

Use the distributive property to multiply x^{4}+2x^{2}+1 by x^{2}-1 and combine like terms.

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