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

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

Evaluate

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

Solution Steps

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

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

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

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

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

$$-\left(x^{4}-4x^{3}+4x^{2}\right)$$

To find the opposite of x^{4}-4x^{3}+4x^{2}, find the opposite of each term.

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

Expand

$$-\left(x^{4}-4x^{3}+4x^{2}\right)$$

Solution Steps

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

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

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

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

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

$$-\left(x^{4}-4x^{3}+4x^{2}\right)$$

To find the opposite of x^{4}-4x^{3}+4x^{2}, find the opposite of each term.

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