Solve (x^2-8)^2-(x^2-8)-56

$$( x ^ { 2 } - 8 ) ^ { 2 } - ( x ^ { 2 } - 8 ) - 56$$

Evaluate

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

Solution Steps

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

$$\left(x^{2}\right)^{2}-16x^{2}+64-\left(x^{2}-8\right)-56$$

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

$$x^{4}-16x^{2}+64-\left(x^{2}-8\right)-56$$

To find the opposite of x^{2}-8, find the opposite of each term.

$$x^{4}-16x^{2}+64-x^{2}+8-56$$

Combine -16x^{2} and -x^{2} to get -17x^{2}.

$$x^{4}-17x^{2}+64+8-56$$

Add 64 and 8 to get 72.

$$x^{4}-17x^{2}+72-56$$

Subtract 56 from 72 to get 16.

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

Expand

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

Solution Steps

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

$$\left(x^{2}\right)^{2}-16x^{2}+64-\left(x^{2}-8\right)-56$$

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

$$x^{4}-16x^{2}+64-\left(x^{2}-8\right)-56$$

To find the opposite of x^{2}-8, find the opposite of each term.

$$x^{4}-16x^{2}+64-x^{2}+8-56$$

Combine -16x^{2} and -x^{2} to get -17x^{2}.

$$x^{4}-17x^{2}+64+8-56$$

Add 64 and 8 to get 72.

$$x^{4}-17x^{2}+72-56$$

Subtract 56 from 72 to get 16.

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