Solve a^2-(ab/2+6a(a-b)/2+(a-b)-a/2)=

$$a ^ { 2 } - ( \frac { a b } { 2 } + \frac { 6 a ( a - b ) } { 2 } + \frac { ( a - b ) - a } { 2 } ) =$$

Evaluate

$$\frac{b+5ab-4a^{2}}{2}$$

Short Solution Steps

Divide 6a\left(a-b\right) by 2 to get 3a\left(a-b\right).

$$a^{2}-\left(\frac{ab}{2}+3a\left(a-b\right)+\frac{a-b-a}{2}\right)$$

Combine a and -a to get 0.

$$a^{2}-\left(\frac{ab}{2}+3a\left(a-b\right)+\frac{-b}{2}\right)$$

To find the opposite of \frac{ab}{2}+3a\left(a-b\right)+\frac{-b}{2}, find the opposite of each term.

$$a^{2}-\frac{ab}{2}-3a\left(a-b\right)-\frac{-b}{2}$$

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

$$\frac{2a^{2}}{2}-\frac{ab}{2}-3a\left(a-b\right)-\frac{-b}{2}$$

Since \frac{2a^{2}}{2} and \frac{ab}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2a^{2}-ab}{2}-3a\left(a-b\right)-\frac{-b}{2}$$

Use the distributive property to multiply -3a by a-b.

$$a^{2}-\frac{ab}{2}-3a^{2}+3ab-\frac{-b}{2}$$

Combine a^{2} and -3a^{2} to get -2a^{2}.

$$-2a^{2}-\frac{ab}{2}+3ab-\frac{-b}{2}$$

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

$$\frac{2\left(-2a^{2}+3ab\right)}{2}-\frac{ab}{2}-\frac{-b}{2}$$

Since \frac{2\left(-2a^{2}+3ab\right)}{2} and \frac{ab}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-2a^{2}+3ab\right)-ab}{2}-\frac{-b}{2}$$

Do the multiplications in 2\left(-2a^{2}+3ab\right)-ab.

$$\frac{-4a^{2}+6ab-ab}{2}-\frac{-b}{2}$$

Combine like terms in -4a^{2}+6ab-ab.

$$\frac{-4a^{2}+5ab}{2}-\frac{-b}{2}$$

Since \frac{-4a^{2}+5ab}{2} and \frac{-b}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4a^{2}+5ab-\left(-b\right)}{2}$$

Do the multiplications in -4a^{2}+5ab-\left(-b\right).

$$\frac{-4a^{2}+5ab+b}{2}$$

Expand

$$\frac{5ab}{2}-2a^{2}+\frac{b}{2}$$

Short Solution Steps

Divide 6a\left(a-b\right) by 2 to get 3a\left(a-b\right).

$$a^{2}-\left(\frac{ab}{2}+3a\left(a-b\right)+\frac{a-b-a}{2}\right)$$

Combine a and -a to get 0.

$$a^{2}-\left(\frac{ab}{2}+3a\left(a-b\right)+\frac{-b}{2}\right)$$

To find the opposite of \frac{ab}{2}+3a\left(a-b\right)+\frac{-b}{2}, find the opposite of each term.

$$a^{2}-\frac{ab}{2}-3a\left(a-b\right)-\frac{-b}{2}$$

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

$$\frac{2a^{2}}{2}-\frac{ab}{2}-3a\left(a-b\right)-\frac{-b}{2}$$

Since \frac{2a^{2}}{2} and \frac{ab}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2a^{2}-ab}{2}-3a\left(a-b\right)-\frac{-b}{2}$$

Use the distributive property to multiply -3a by a-b.

$$a^{2}-\frac{ab}{2}-3a^{2}+3ab-\frac{-b}{2}$$

Combine a^{2} and -3a^{2} to get -2a^{2}.

$$-2a^{2}-\frac{ab}{2}+3ab-\frac{-b}{2}$$

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

$$\frac{2\left(-2a^{2}+3ab\right)}{2}-\frac{ab}{2}-\frac{-b}{2}$$

Since \frac{2\left(-2a^{2}+3ab\right)}{2} and \frac{ab}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-2a^{2}+3ab\right)-ab}{2}-\frac{-b}{2}$$

Do the multiplications in 2\left(-2a^{2}+3ab\right)-ab.

$$\frac{-4a^{2}+6ab-ab}{2}-\frac{-b}{2}$$

Combine like terms in -4a^{2}+6ab-ab.

$$\frac{-4a^{2}+5ab}{2}-\frac{-b}{2}$$

Since \frac{-4a^{2}+5ab}{2} and \frac{-b}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4a^{2}+5ab-\left(-b\right)}{2}$$

Do the multiplications in -4a^{2}+5ab-\left(-b\right).

$$\frac{-4a^{2}+5ab+b}{2}$$