Solve (2x-1)^2-4(x-1)(x+1)+4(x-2)

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

Evaluate

$$-3$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.

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

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

$$4x^{2}-4x+1-4\left(x-1\right)\left(x+1\right)+4x-8$$

Use the distributive property to multiply -4 by x-1.

$$4x^{2}-4x+1+\left(-4x+4\right)\left(x+1\right)+4x-8$$

Use the distributive property to multiply -4x+4 by x+1 and combine like terms.

$$4x^{2}-4x+1-4x^{2}+4+4x-8$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-4x+1+4+4x-8$$

Add 1 and 4 to get 5.

$$-4x+5+4x-8$$

Combine -4x and 4x to get 0.

$$5-8$$

Subtract 8 from 5 to get -3.

$$-3$$

Factor

$$-3$$