Solve (x^2+1)^2-7(x^2+1)+10

$$( x ^ { 2 } + 1 ) ^ { 2 } - 7 ( x ^ { 2 } + 1 ) + 10$$

Evaluate

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

Solution Steps

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

$$\left(x^{2}\right)^{2}+2x^{2}+1-7\left(x^{2}+1\right)+10$$

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

$$x^{4}+2x^{2}+1-7\left(x^{2}+1\right)+10$$

Use the distributive property to multiply -7 by x^{2}+1.

$$x^{4}+2x^{2}+1-7x^{2}-7+10$$

Combine 2x^{2} and -7x^{2} to get -5x^{2}.

$$x^{4}-5x^{2}+1-7+10$$

Subtract 7 from 1 to get -6.

$$x^{4}-5x^{2}-6+10$$

Add -6 and 10 to get 4.

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

Expand

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

Solution Steps

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

$$\left(x^{2}\right)^{2}+2x^{2}+1-7\left(x^{2}+1\right)+10$$

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

$$x^{4}+2x^{2}+1-7\left(x^{2}+1\right)+10$$

Use the distributive property to multiply -7 by x^{2}+1.

$$x^{4}+2x^{2}+1-7x^{2}-7+10$$

Combine 2x^{2} and -7x^{2} to get -5x^{2}.

$$x^{4}-5x^{2}+1-7+10$$

Subtract 7 from 1 to get -6.

$$x^{4}-5x^{2}-6+10$$

Add -6 and 10 to get 4.

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