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

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

Evaluate

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

Solution Steps

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

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

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

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

Apply the distributive property by multiplying each term of -\frac{1}{2}x+\frac{1}{2} by each term of x+3.

$$-\frac{1}{2}xx-\frac{1}{2}x\times 3+\frac{1}{2}x+\frac{1}{2}\times 3$$

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

$$-\frac{1}{2}x^{2}-\frac{1}{2}x\times 3+\frac{1}{2}x+\frac{1}{2}\times 3$$

Express -\frac{1}{2}\times 3 as a single fraction.

$$-\frac{1}{2}x^{2}+\frac{-3}{2}x+\frac{1}{2}x+\frac{1}{2}\times 3$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-\frac{1}{2}x^{2}-\frac{3}{2}x+\frac{1}{2}x+\frac{1}{2}\times 3$$

Combine -\frac{3}{2}x and \frac{1}{2}x to get -x.

$$-\frac{1}{2}x^{2}-x+\frac{1}{2}\times 3$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$-\frac{1}{2}x^{2}-x+\frac{3}{2}$$

Expand

$$-\frac{x^{2}}{2}-x+\frac{3}{2}$$

Solution Steps

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

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

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

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

Apply the distributive property by multiplying each term of -\frac{1}{2}x+\frac{1}{2} by each term of x+3.

$$-\frac{1}{2}xx-\frac{1}{2}x\times 3+\frac{1}{2}x+\frac{1}{2}\times 3$$

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

$$-\frac{1}{2}x^{2}-\frac{1}{2}x\times 3+\frac{1}{2}x+\frac{1}{2}\times 3$$

Express -\frac{1}{2}\times 3 as a single fraction.

$$-\frac{1}{2}x^{2}+\frac{-3}{2}x+\frac{1}{2}x+\frac{1}{2}\times 3$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-\frac{1}{2}x^{2}-\frac{3}{2}x+\frac{1}{2}x+\frac{1}{2}\times 3$$

Combine -\frac{3}{2}x and \frac{1}{2}x to get -x.

$$-\frac{1}{2}x^{2}-x+\frac{1}{2}\times 3$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$-\frac{1}{2}x^{2}-x+\frac{3}{2}$$