Solve left(x^2-100right)^2+5

$${ \left( { x }^{ 2 } -100 \right) }^{ 2 } +5$$

Expand

$$x^{4}-200x^{2}+10005$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-100\right)^{2}.

$$\left(x^{2}\right)^{2}-200x^{2}+10000+5$$

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

$$x^{4}-200x^{2}+10000+5$$

Add 10000 and 5 to get 10005.

$$x^{4}-200x^{2}+10005$$

Evaluate

$$\left(x^{2}-100\right)^{2}+5$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-100\right)^{2}.

$$\left(x^{2}\right)^{2}-200x^{2}+10000+5$$

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

$$x^{4}-200x^{2}+10000+5$$

Add 10000 and 5 to get 10005.

$$x^{4}-200x^{2}+10005$$