Solve (-a+1/2)*3^2+2*a+1/2*3+a+1/2

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

Evaluate

$$-\left(a+1\right)$$

Short Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\left(-\frac{a+1}{2}\right)\times 9+2\times \frac{a+1}{2}\times 3+\frac{a+1}{2}$$

Express \left(-\frac{a+1}{2}\right)\times 9 as a single fraction.

$$\frac{-\left(a+1\right)\times 9}{2}+2\times \frac{a+1}{2}\times 3+\frac{a+1}{2}$$

Multiply 2 and 3 to get 6.

$$\frac{-\left(a+1\right)\times 9}{2}+6\times \frac{a+1}{2}+\frac{a+1}{2}$$

Cancel out 2, the greatest common factor in 6 and 2.

$$\frac{-\left(a+1\right)\times 9}{2}+3\left(a+1\right)+\frac{a+1}{2}$$

Use the distributive property to multiply 3 by a+1.

$$\frac{-\left(a+1\right)\times 9}{2}+3a+3+\frac{a+1}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3a+3 times \frac{2}{2}.

$$\frac{-\left(a+1\right)\times 9}{2}+\frac{2\left(3a+3\right)}{2}+\frac{a+1}{2}$$

Since \frac{-\left(a+1\right)\times 9}{2} and \frac{2\left(3a+3\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\left(a+1\right)\times 9+2\left(3a+3\right)}{2}+\frac{a+1}{2}$$

Do the multiplications in -\left(a+1\right)\times 9+2\left(3a+3\right).

$$\frac{-9a-9+6a+6}{2}+\frac{a+1}{2}$$

Combine like terms in -9a-9+6a+6.

$$\frac{-3a-3}{2}+\frac{a+1}{2}$$

Since \frac{-3a-3}{2} and \frac{a+1}{2} have the same denominator, add them by adding their numerators.

$$\frac{-3a-3+a+1}{2}$$

Combine like terms in -3a-3+a+1.

$$\frac{-2a-2}{2}$$

Divide each term of -2a-2 by 2 to get -1-a.

$$-1-a$$

Expand

$$-\left(a+1\right)$$

Short Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\left(-\frac{a+1}{2}\right)\times 9+2\times \frac{a+1}{2}\times 3+\frac{a+1}{2}$$

Express \left(-\frac{a+1}{2}\right)\times 9 as a single fraction.

$$\frac{-\left(a+1\right)\times 9}{2}+2\times \frac{a+1}{2}\times 3+\frac{a+1}{2}$$

Multiply 2 and 3 to get 6.

$$\frac{-\left(a+1\right)\times 9}{2}+6\times \frac{a+1}{2}+\frac{a+1}{2}$$

Cancel out 2, the greatest common factor in 6 and 2.

$$\frac{-\left(a+1\right)\times 9}{2}+3\left(a+1\right)+\frac{a+1}{2}$$

Use the distributive property to multiply 3 by a+1.

$$\frac{-\left(a+1\right)\times 9}{2}+3a+3+\frac{a+1}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3a+3 times \frac{2}{2}.

$$\frac{-\left(a+1\right)\times 9}{2}+\frac{2\left(3a+3\right)}{2}+\frac{a+1}{2}$$

Since \frac{-\left(a+1\right)\times 9}{2} and \frac{2\left(3a+3\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\left(a+1\right)\times 9+2\left(3a+3\right)}{2}+\frac{a+1}{2}$$

Do the multiplications in -\left(a+1\right)\times 9+2\left(3a+3\right).

$$\frac{-9a-9+6a+6}{2}+\frac{a+1}{2}$$

Combine like terms in -9a-9+6a+6.

$$\frac{-3a-3}{2}+\frac{a+1}{2}$$

Since \frac{-3a-3}{2} and \frac{a+1}{2} have the same denominator, add them by adding their numerators.

$$\frac{-3a-3+a+1}{2}$$

Combine like terms in -3a-3+a+1.

$$\frac{-2a-2}{2}$$

Divide each term of -2a-2 by 2 to get -1-a.

$$-1-a$$