Solve [-x^2+2x-1]^2

$$[ - x ^ { 2 } + 2 x - 1 ] ^ { 2 }$$

Evaluate

$$\left(x-1\right)^{4}$$

Solution Steps

Square -x^{2}+2x-1.

$$4x^{2}-2\left(-x^{2}\right)+4x\left(-x^{2}\right)-4x+\left(-x^{2}\right)^{2}+1$$

Multiply -2 and -1 to get 2.

$$4x^{2}+2x^{2}+4x\left(-x^{2}\right)-4x+\left(-x^{2}\right)^{2}+1$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+4x\left(-x^{2}\right)-4x+\left(-x^{2}\right)^{2}+1$$

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

$$6x^{2}+4x\left(-x^{2}\right)-4x+\left(x^{2}\right)^{2}+1$$

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

$$6x^{2}+4x\left(-x^{2}\right)-4x+x^{4}+1$$

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

$$6x^{2}+4x^{3}\left(-1\right)-4x+x^{4}+1$$

Multiply 4 and -1 to get -4.

$$6x^{2}-4x^{3}-4x+x^{4}+1$$

Expand

$$x^{4}-4x^{3}+6x^{2}-4x+1$$

Solution Steps

Square -x^{2}+2x-1.

$$4x^{2}-2\left(-x^{2}\right)+4x\left(-x^{2}\right)-4x+\left(-x^{2}\right)^{2}+1$$

Multiply -2 and -1 to get 2.

$$4x^{2}+2x^{2}+4x\left(-x^{2}\right)-4x+\left(-x^{2}\right)^{2}+1$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+4x\left(-x^{2}\right)-4x+\left(-x^{2}\right)^{2}+1$$

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

$$6x^{2}+4x\left(-x^{2}\right)-4x+\left(x^{2}\right)^{2}+1$$

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

$$6x^{2}+4x\left(-x^{2}\right)-4x+x^{4}+1$$

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

$$6x^{2}+4x^{3}\left(-1\right)-4x+x^{4}+1$$

Multiply 4 and -1 to get -4.

$$6x^{2}-4x^{3}-4x+x^{4}+1$$