Solve (x^2-x)^2-4(x^2-x)+4

$$( x ^ { 2 } - x ) ^ { 2 } - 4 ( x ^ { 2 } - x ) + 4$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply -4 by x^{2}-x.

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

Combine x^{2} and -4x^{2} to get -3x^{2}.

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

Expand

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

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply -4 by x^{2}-x.

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

Combine x^{2} and -4x^{2} to get -3x^{2}.

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