Solve -(8-a)-[-(a+2b-1)+(-1/aab)]-[3/2a^2+(1/2b+1)+1/aab]

$$- ( 8 - a ) - [ - ( a + 2 b - 1 ) + ( - \frac { 1 } { a } a b ) ] - [ \frac { 3 } { 2 } a ^ { 2 } + ( \frac { 1 } { 2 } b + 1 ) + \frac { 1 } { a } a b ]$$

Evaluate

$$-\frac{3a^{2}}{2}+\frac{3b}{2}+2a-10$$

Solution Steps

To find the opposite of 8-a, find the opposite of each term.

$$-8+a-\left(-\left(a+2b-1\right)+\left(-\frac{1}{a}\right)ab\right)-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

To find the opposite of a+2b-1, find the opposite of each term.

$$-8+a-\left(-a-2b+1+\left(-\frac{1}{a}\right)ab\right)-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

Cancel out a and a.

$$-8+a-\left(-a-2b+1-b\right)-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

Combine -2b and -b to get -3b.

$$-8+a-\left(-a-3b+1\right)-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

To find the opposite of -a-3b+1, find the opposite of each term.

$$-8+a+a+3b-1-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

Combine a and a to get 2a.

$$-8+2a+3b-1-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

Subtract 1 from -8 to get -9.

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

Cancel out a and a.

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

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

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

To find the opposite of \frac{3}{2}a^{2}+\frac{3}{2}b+1, find the opposite of each term.

$$-9+2a+3b-\frac{3}{2}a^{2}-\frac{3}{2}b-1$$

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

$$-9+2a+\frac{3}{2}b-\frac{3}{2}a^{2}-1$$

Subtract 1 from -9 to get -10.

$$-10+2a+\frac{3}{2}b-\frac{3}{2}a^{2}$$

Expand

$$-\frac{3a^{2}}{2}+\frac{3b}{2}+2a-10$$

Solution Steps

To find the opposite of 8-a, find the opposite of each term.

$$-8+a-\left(-\left(a+2b-1\right)+\left(-\frac{1}{a}\right)ab\right)-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

To find the opposite of a+2b-1, find the opposite of each term.

$$-8+a-\left(-a-2b+1+\left(-\frac{1}{a}\right)ab\right)-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

Cancel out a and a.

$$-8+a-\left(-a-2b+1-b\right)-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

Combine -2b and -b to get -3b.

$$-8+a-\left(-a-3b+1\right)-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

To find the opposite of -a-3b+1, find the opposite of each term.

$$-8+a+a+3b-1-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

Combine a and a to get 2a.

$$-8+2a+3b-1-\left(\frac{3}{2}a^{2}+\frac{1}{2}b+1+\frac{1}{a}ab\right)$$

Subtract 1 from -8 to get -9.

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

Cancel out a and a.

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

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

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

To find the opposite of \frac{3}{2}a^{2}+\frac{3}{2}b+1, find the opposite of each term.

$$-9+2a+3b-\frac{3}{2}a^{2}-\frac{3}{2}b-1$$

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

$$-9+2a+\frac{3}{2}b-\frac{3}{2}a^{2}-1$$

Subtract 1 from -9 to get -10.

$$-10+2a+\frac{3}{2}b-\frac{3}{2}a^{2}$$