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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2+3x.

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

Cancel out 2 and 2.

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

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

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2+3x.

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

Cancel out 2 and 2.

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

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

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

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

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

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

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

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

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

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

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