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

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

Evaluate

$$\left(x-2\right)\left(x-2k+1\right)$$

Solution Steps

Use the distributive property to multiply 2k+1 by x.

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

To find the opposite of 2kx+x, find the opposite of each term.

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

Use the distributive property to multiply 4 by k-\frac{1}{2}.

$$x^{2}-2kx-x+4k-2$$

Expand

$$x^{2}-2kx-x+4k-2$$

Solution Steps

Use the distributive property to multiply 2k+1 by x.

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

To find the opposite of 2kx+x, find the opposite of each term.

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

Use the distributive property to multiply 4 by k-\frac{1}{2}.

$$x^{2}-2kx-x+4k-2$$