Solve 4xleft(x-1right)^-left(2x-1right)^2

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

Evaluate

$$-1$$

Solution Steps

Calculate x-1 to the power of 1 and get x-1.

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

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

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

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

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

To find the opposite of 4x^{2}-4x+1, find the opposite of each term.

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

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

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

Combine -4x and 4x to get 0.

$$-1$$

Factor

$$-1$$