Solve (x^2-2x)^2-64

$$( x ^ { 2 } - 2 x ) ^ { 2 } - 64$$

Evaluate

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

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-4x^{3}+4x^{2}-64$$

Expand

$$x^{4}-4x^{3}+4x^{2}-64$$

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-4x^{3}+4x^{2}-64$$