Solve 18ab^{3}-(-4ab)(-3b^2)+(+15a^3b^4):(-3a^2b

$$18 a b ^ { 3 } - ( - 4 a b ) ( - 3 b ^ { 2 } ) + ( + 15 a ^ { 3 } b ^ { 4 } ) : ( - 3 a ^ { 2 } b$$

Evaluate

$$ab^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$18ab^{3}-\left(-4ab^{3}\left(-3\right)\right)+\frac{15a^{3}b^{4}}{-3a^{2}b}$$

Multiply -4 and -3 to get 12.

$$18ab^{3}-12ab^{3}+\frac{15a^{3}b^{4}}{-3a^{2}b}$$

Combine 18ab^{3} and -12ab^{3} to get 6ab^{3}.

$$6ab^{3}+\frac{15a^{3}b^{4}}{-3a^{2}b}$$

Cancel out 3ba^{2} in both numerator and denominator.

$$6ab^{3}+\frac{5ab^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$6ab^{3}-5ab^{3}$$

Combine 6ab^{3} and -5ab^{3} to get ab^{3}.

$$ab^{3}$$

Differentiate w.r.t. a

$$b^{3}$$