Solve (24a^{3}b^{2}-16a^{2}b^3+6a^2b^2)div(-2ab)^2

$$( 24 a ^ { 3 } b ^ { 2 } - 16 a ^ { 2 } b ^ { 3 } + 6 a ^ { 2 } b ^ { 2 } ) \div ( - 2 a b ) ^ { 2 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{24a^{3}b^{2}-16a^{2}b^{3}+6a^{2}b^{2}}{\left(-2\right)^{2}a^{2}b^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{24a^{3}b^{2}-16a^{2}b^{3}+6a^{2}b^{2}}{4a^{2}b^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2\left(12a-8b+3\right)a^{2}b^{2}}{4a^{2}b^{2}}$$

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

$$\frac{12a-8b+3}{2}$$

Expand

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

Short Solution Steps

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

$$\frac{24a^{3}b^{2}-16a^{2}b^{3}+6a^{2}b^{2}}{\left(-2\right)^{2}a^{2}b^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{24a^{3}b^{2}-16a^{2}b^{3}+6a^{2}b^{2}}{4a^{2}b^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2\left(12a-8b+3\right)a^{2}b^{2}}{4a^{2}b^{2}}$$

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

$$\frac{12a-8b+3}{2}$$