Solve 5a^{2}b-[12a^3(-b)^2-a(-3a)^2*(-3b)^2]:(-23ab)

$$5 a ^ { 2 } b - [ 12 a ^ { 3 } ( - b ) ^ { 2 } - a ( - 3 a ) ^ { 2 } \cdot ( - 3 b ) ^ { 2 } ] : ( - 23 a b )$$

Evaluate

$$2ba^{2}$$

Solution Steps

Calculate -b to the power of 2 and get b^{2}.

$$5a^{2}b-\frac{12a^{3}b^{2}-a\left(-3a\right)^{2}\left(-3b\right)^{2}}{-23ab}$$

Expand \left(-3a\right)^{2}.

$$5a^{2}b-\frac{12a^{3}b^{2}-a\left(-3\right)^{2}a^{2}\left(-3b\right)^{2}}{-23ab}$$

Calculate -3 to the power of 2 and get 9.

$$5a^{2}b-\frac{12a^{3}b^{2}-a\times 9a^{2}\left(-3b\right)^{2}}{-23ab}$$

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

$$5a^{2}b-\frac{12a^{3}b^{2}-a^{3}\times 9\left(-3b\right)^{2}}{-23ab}$$

Expand \left(-3b\right)^{2}.

$$5a^{2}b-\frac{12a^{3}b^{2}-a^{3}\times 9\left(-3\right)^{2}b^{2}}{-23ab}$$

Calculate -3 to the power of 2 and get 9.

$$5a^{2}b-\frac{12a^{3}b^{2}-a^{3}\times 9\times 9b^{2}}{-23ab}$$

Multiply 9 and 9 to get 81.

$$5a^{2}b-\frac{12a^{3}b^{2}-a^{3}\times 81b^{2}}{-23ab}$$

Combine 12a^{3}b^{2} and -a^{3}\times 81b^{2} to get -69a^{3}b^{2}.

$$5a^{2}b-\frac{-69a^{3}b^{2}}{-23ab}$$

Cancel out 23ab in both numerator and denominator.

$$5a^{2}b-\frac{-3ba^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$5a^{2}b-3ba^{2}$$

Combine 5a^{2}b and -3ba^{2} to get 2a^{2}b.

$$2a^{2}b$$

Expand

$$2ba^{2}$$

Solution Steps

Calculate -b to the power of 2 and get b^{2}.

$$5a^{2}b-\frac{12a^{3}b^{2}-a\left(-3a\right)^{2}\left(-3b\right)^{2}}{-23ab}$$

Expand \left(-3a\right)^{2}.

$$5a^{2}b-\frac{12a^{3}b^{2}-a\left(-3\right)^{2}a^{2}\left(-3b\right)^{2}}{-23ab}$$

Calculate -3 to the power of 2 and get 9.

$$5a^{2}b-\frac{12a^{3}b^{2}-a\times 9a^{2}\left(-3b\right)^{2}}{-23ab}$$

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

$$5a^{2}b-\frac{12a^{3}b^{2}-a^{3}\times 9\left(-3b\right)^{2}}{-23ab}$$

Expand \left(-3b\right)^{2}.

$$5a^{2}b-\frac{12a^{3}b^{2}-a^{3}\times 9\left(-3\right)^{2}b^{2}}{-23ab}$$

Calculate -3 to the power of 2 and get 9.

$$5a^{2}b-\frac{12a^{3}b^{2}-a^{3}\times 9\times 9b^{2}}{-23ab}$$

Multiply 9 and 9 to get 81.

$$5a^{2}b-\frac{12a^{3}b^{2}-a^{3}\times 81b^{2}}{-23ab}$$

Combine 12a^{3}b^{2} and -a^{3}\times 81b^{2} to get -69a^{3}b^{2}.

$$5a^{2}b-\frac{-69a^{3}b^{2}}{-23ab}$$

Cancel out 23ab in both numerator and denominator.

$$5a^{2}b-\frac{-3ba^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$5a^{2}b-3ba^{2}$$

Combine 5a^{2}b and -3ba^{2} to get 2a^{2}b.

$$2a^{2}b$$