Solve (-1/3ab)^2[ab(2a-3b)-2a(ab-b^2)]

$$( - \frac { 1 } { 3 } a b ) ^ { 2 } [ a b ( 2 a - 3 b ) - 2 a ( a b - b ^ { 2 } ) ]$$

Evaluate

$$-\frac{a^{3}b^{4}}{9}$$

Solution Steps

Expand \left(-\frac{1}{3}ab\right)^{2}.

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

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}a^{2}b^{2}\left(ab\left(2a-3b\right)-2a\left(ab-b^{2}\right)\right)$$

Use the distributive property to multiply ab by 2a-3b.

$$\frac{1}{9}a^{2}b^{2}\left(2ba^{2}-3ab^{2}-2a\left(ab-b^{2}\right)\right)$$

Use the distributive property to multiply -2a by ab-b^{2}.

$$\frac{1}{9}a^{2}b^{2}\left(2ba^{2}-3ab^{2}-2ba^{2}+2ab^{2}\right)$$

Combine 2ba^{2} and -2ba^{2} to get 0.

$$\frac{1}{9}a^{2}b^{2}\left(-3ab^{2}+2ab^{2}\right)$$

Combine -3ab^{2} and 2ab^{2} to get -ab^{2}.

$$\frac{1}{9}a^{2}b^{2}\left(-1\right)ab^{2}$$

Multiply \frac{1}{9} and -1 to get -\frac{1}{9}.

$$-\frac{1}{9}a^{2}b^{2}ab^{2}$$

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

$$-\frac{1}{9}a^{3}b^{2}b^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-\frac{1}{9}a^{3}b^{4}$$

Expand

$$-\frac{a^{3}b^{4}}{9}$$

Solution Steps

Expand \left(-\frac{1}{3}ab\right)^{2}.

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

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}a^{2}b^{2}\left(ab\left(2a-3b\right)-2a\left(ab-b^{2}\right)\right)$$

Use the distributive property to multiply ab by 2a-3b.

$$\frac{1}{9}a^{2}b^{2}\left(2ba^{2}-3ab^{2}-2a\left(ab-b^{2}\right)\right)$$

Use the distributive property to multiply -2a by ab-b^{2}.

$$\frac{1}{9}a^{2}b^{2}\left(2ba^{2}-3ab^{2}-2ba^{2}+2ab^{2}\right)$$

Combine 2ba^{2} and -2ba^{2} to get 0.

$$\frac{1}{9}a^{2}b^{2}\left(-3ab^{2}+2ab^{2}\right)$$

Combine -3ab^{2} and 2ab^{2} to get -ab^{2}.

$$\frac{1}{9}a^{2}b^{2}\left(-1\right)ab^{2}$$

Multiply \frac{1}{9} and -1 to get -\frac{1}{9}.

$$-\frac{1}{9}a^{2}b^{2}ab^{2}$$

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

$$-\frac{1}{9}a^{3}b^{2}b^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-\frac{1}{9}a^{3}b^{4}$$