Solve (-18a^{4}b^{2}):(-3ab)+(-10ab)*(1/2ab)-(-8a^6b^6):(-2a^3b^5)=

$$( - 18 a ^ { 4 } b ^ { 2 } ) : ( - 3 a b ) + ( - 10 a b ) \cdot ( \frac { 1 } { 2 } a b ) - ( - 8 a ^ { 6 } b ^ { 6 } ) : ( - 2 a ^ { 3 } b ^ { 5 } ) =$$

Factor

$$b\left(2a-5b\right)a^{2}$$

Solution Steps

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

$$factor(\frac{-18a^{4}b^{2}}{-3ab}-10a^{2}b\times \frac{1}{2}b-\frac{-8a^{6}b^{6}}{-2a^{3}b^{5}})$$

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

$$factor(\frac{-18a^{4}b^{2}}{-3ab}-10a^{2}b^{2}\times \frac{1}{2}-\frac{-8a^{6}b^{6}}{-2a^{3}b^{5}})$$

Cancel out 3ab in both numerator and denominator.

$$factor(\frac{-6ba^{3}}{-1}-10a^{2}b^{2}\times \frac{1}{2}-\frac{-8a^{6}b^{6}}{-2a^{3}b^{5}})$$

Anything divided by -1 gives its opposite.

$$factor(6ba^{3}-10a^{2}b^{2}\times \frac{1}{2}-\frac{-8a^{6}b^{6}}{-2a^{3}b^{5}})$$

Multiply -10 and \frac{1}{2} to get -5.

$$factor(6ba^{3}-5a^{2}b^{2}-\frac{-8a^{6}b^{6}}{-2a^{3}b^{5}})$$

Cancel out 2a^{3}b^{5} in both numerator and denominator.

$$factor(6ba^{3}-5a^{2}b^{2}-\frac{-4ba^{3}}{-1})$$

Anything divided by -1 gives its opposite.

$$factor(6ba^{3}-5a^{2}b^{2}-4ba^{3})$$

Combine 6ba^{3} and -4ba^{3} to get 2ba^{3}.

$$factor(2ba^{3}-5a^{2}b^{2})$$

Factor out ba^{2}.

$$ba^{2}\left(2a-5b\right)$$

Evaluate

$$b\left(2a-5b\right)a^{2}$$