Solve =-2a+1/2(x-1)(2x+1)-2(x-3)(x)

$$= - 2 a + \frac { 1 } { 2 } ( x - 1 ) ( 2 x + 1 ) - 2 ( x - 3 ) ( x )$$

Evaluate

$$-x^{2}+\frac{11x}{2}-2a-\frac{1}{2}$$

Solution Steps

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

$$-2a+\left(\frac{1}{2}x+\frac{1}{2}\left(-1\right)\right)\left(2x+1\right)-2\left(x-3\right)x$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$-2a+\left(\frac{1}{2}x-\frac{1}{2}\right)\left(2x+1\right)-2\left(x-3\right)x$$

Apply the distributive property by multiplying each term of \frac{1}{2}x-\frac{1}{2} by each term of 2x+1.

$$-2a+\frac{1}{2}x\times 2x+\frac{1}{2}x-\frac{1}{2}\times 2x-\frac{1}{2}-2\left(x-3\right)x$$

Multiply x and x to get x^{2}.

$$-2a+\frac{1}{2}x^{2}\times 2+\frac{1}{2}x-\frac{1}{2}\times 2x-\frac{1}{2}-2\left(x-3\right)x$$

Cancel out 2 and 2.

$$-2a+x^{2}+\frac{1}{2}x-\frac{1}{2}\times 2x-\frac{1}{2}-2\left(x-3\right)x$$

Cancel out 2 and 2.

$$-2a+x^{2}+\frac{1}{2}x-x-\frac{1}{2}-2\left(x-3\right)x$$

Combine \frac{1}{2}x and -x to get -\frac{1}{2}x.

$$-2a+x^{2}-\frac{1}{2}x-\frac{1}{2}-2\left(x-3\right)x$$

Use the distributive property to multiply -2 by x-3.

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

Use the distributive property to multiply -2x+6 by x.

$$-2a+x^{2}-\frac{1}{2}x-\frac{1}{2}-2x^{2}+6x$$

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

$$-2a-x^{2}-\frac{1}{2}x-\frac{1}{2}+6x$$

Combine -\frac{1}{2}x and 6x to get \frac{11}{2}x.

$$-2a-x^{2}+\frac{11}{2}x-\frac{1}{2}$$

Expand

$$-x^{2}+\frac{11x}{2}-2a-\frac{1}{2}$$

Solution Steps

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

$$-2a+\left(\frac{1}{2}x+\frac{1}{2}\left(-1\right)\right)\left(2x+1\right)-2\left(x-3\right)x$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$-2a+\left(\frac{1}{2}x-\frac{1}{2}\right)\left(2x+1\right)-2\left(x-3\right)x$$

Apply the distributive property by multiplying each term of \frac{1}{2}x-\frac{1}{2} by each term of 2x+1.

$$-2a+\frac{1}{2}x\times 2x+\frac{1}{2}x-\frac{1}{2}\times 2x-\frac{1}{2}-2\left(x-3\right)x$$

Multiply x and x to get x^{2}.

$$-2a+\frac{1}{2}x^{2}\times 2+\frac{1}{2}x-\frac{1}{2}\times 2x-\frac{1}{2}-2\left(x-3\right)x$$

Cancel out 2 and 2.

$$-2a+x^{2}+\frac{1}{2}x-\frac{1}{2}\times 2x-\frac{1}{2}-2\left(x-3\right)x$$

Cancel out 2 and 2.

$$-2a+x^{2}+\frac{1}{2}x-x-\frac{1}{2}-2\left(x-3\right)x$$

Combine \frac{1}{2}x and -x to get -\frac{1}{2}x.

$$-2a+x^{2}-\frac{1}{2}x-\frac{1}{2}-2\left(x-3\right)x$$

Use the distributive property to multiply -2 by x-3.

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

Use the distributive property to multiply -2x+6 by x.

$$-2a+x^{2}-\frac{1}{2}x-\frac{1}{2}-2x^{2}+6x$$

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

$$-2a-x^{2}-\frac{1}{2}x-\frac{1}{2}+6x$$

Combine -\frac{1}{2}x and 6x to get \frac{11}{2}x.

$$-2a-x^{2}+\frac{11}{2}x-\frac{1}{2}$$