Solve [(2ab-3ab)^2:(2ab)]*a^2b-3a^3b^2

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

Evaluate

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

Short Solution Steps

Combine 2ab and -3ab to get -ab.

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

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

$$\frac{\left(-1\right)^{2}a^{2}b^{2}}{2ab}a^{2}b-3a^{3}b^{2}$$

Calculate -1 to the power of 2 and get 1.

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

Cancel out ab in both numerator and denominator.

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

Express \frac{ab}{2}a^{2} as a single fraction.

$$\frac{aba^{2}}{2}b-3a^{3}b^{2}$$

Express \frac{aba^{2}}{2}b as a single fraction.

$$\frac{aba^{2}b}{2}-3a^{3}b^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3a^{3}b^{2} times \frac{2}{2}.

$$\frac{aba^{2}b}{2}-\frac{2\times 3a^{3}b^{2}}{2}$$

Since \frac{aba^{2}b}{2} and \frac{2\times 3a^{3}b^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aba^{2}b-2\times 3a^{3}b^{2}}{2}$$

Do the multiplications in aba^{2}b-2\times 3a^{3}b^{2}.

$$\frac{a^{3}b^{2}-6a^{3}b^{2}}{2}$$

Combine like terms in a^{3}b^{2}-6a^{3}b^{2}.

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

Expand

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

Short Solution Steps

Combine 2ab and -3ab to get -ab.

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

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

$$\frac{\left(-1\right)^{2}a^{2}b^{2}}{2ab}a^{2}b-3a^{3}b^{2}$$

Calculate -1 to the power of 2 and get 1.

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

Cancel out ab in both numerator and denominator.

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

Express \frac{ab}{2}a^{2} as a single fraction.

$$\frac{aba^{2}}{2}b-3a^{3}b^{2}$$

Express \frac{aba^{2}}{2}b as a single fraction.

$$\frac{aba^{2}b}{2}-3a^{3}b^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3a^{3}b^{2} times \frac{2}{2}.

$$\frac{aba^{2}b}{2}-\frac{2\times 3a^{3}b^{2}}{2}$$

Since \frac{aba^{2}b}{2} and \frac{2\times 3a^{3}b^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aba^{2}b-2\times 3a^{3}b^{2}}{2}$$

Do the multiplications in aba^{2}b-2\times 3a^{3}b^{2}.

$$\frac{a^{3}b^{2}-6a^{3}b^{2}}{2}$$

Combine like terms in a^{3}b^{2}-6a^{3}b^{2}.

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