Solve (x^2+1)^2-6(x^2+1)+8=

$$( x ^ { 2 } + 1 ) ^ { 2 } - 6 ( x ^ { 2 } + 1 ) + 8 =$$

Evaluate

$$x^{4}-4x^{2}+3$$

Solution Steps

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

$$\left(x^{2}\right)^{2}+2x^{2}+1-6\left(x^{2}+1\right)+8$$

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

$$x^{4}+2x^{2}+1-6\left(x^{2}+1\right)+8$$

Use the distributive property to multiply -6 by x^{2}+1.

$$x^{4}+2x^{2}+1-6x^{2}-6+8$$

Combine 2x^{2} and -6x^{2} to get -4x^{2}.

$$x^{4}-4x^{2}+1-6+8$$

Subtract 6 from 1 to get -5.

$$x^{4}-4x^{2}-5+8$$

Add -5 and 8 to get 3.

$$x^{4}-4x^{2}+3$$

Expand

$$x^{4}-4x^{2}+3$$

Solution Steps

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

$$\left(x^{2}\right)^{2}+2x^{2}+1-6\left(x^{2}+1\right)+8$$

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

$$x^{4}+2x^{2}+1-6\left(x^{2}+1\right)+8$$

Use the distributive property to multiply -6 by x^{2}+1.

$$x^{4}+2x^{2}+1-6x^{2}-6+8$$

Combine 2x^{2} and -6x^{2} to get -4x^{2}.

$$x^{4}-4x^{2}+1-6+8$$

Subtract 6 from 1 to get -5.

$$x^{4}-4x^{2}-5+8$$

Add -5 and 8 to get 3.

$$x^{4}-4x^{2}+3$$