Solve [(-1/2ab)(-1/2ab)]:[(-1/2ab)(-1/2ab)]-frac{1}{8}a

$$[ ( - \frac { 1 } { 2 } a b ) ( - \frac { 1 } { 2 } a b ) ] : [ ( - \frac { 1 } { 2 } a b ) ( - \frac { 1 } { 2 } a b ) ] - \frac { 1 } { 8 } a$$

Evaluate

$$-\frac{a}{8}+1$$

Solution Steps

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

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

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

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

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

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

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

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

Divide -\frac{1}{2}a^{2}b^{2}\left(-\frac{1}{2}\right) by -\frac{1}{2}a^{2}b^{2}\left(-\frac{1}{2}\right) to get 1.

$$1-\frac{1}{8}a$$

Factor

$$\frac{8-a}{8}$$

Solution Steps

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

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

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

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

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

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

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

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

Divide -\frac{1}{2}a^{2}b^{2}\left(-\frac{1}{2}\right) by -\frac{1}{2}a^{2}b^{2}\left(-\frac{1}{2}\right) to get 1.

$$factor(1-\frac{1}{8}a)$$

Factor out \frac{1}{8}.

$$\frac{8-a}{8}$$