Solve (x^2+8)^2-81

$$( x ^ { 2 } + 8 ) ^ { 2 } - 81$$

Evaluate

$$x^{4}+16x^{2}-17$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+8\right)^{2}.

$$\left(x^{2}\right)^{2}+16x^{2}+64-81$$

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

$$x^{4}+16x^{2}+64-81$$

Subtract 81 from 64 to get -17.

$$x^{4}+16x^{2}-17$$

Expand

$$x^{4}+16x^{2}-17$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+8\right)^{2}.

$$\left(x^{2}\right)^{2}+16x^{2}+64-81$$

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

$$x^{4}+16x^{2}+64-81$$

Subtract 81 from 64 to get -17.

$$x^{4}+16x^{2}-17$$