Solve -9a^3(-ab-ab/3)(b/3-3b)

$$- 9 a ^ { 3 } ( - a b - \frac { a b } { 3 } ) ( \frac { b } { 3 } - 3 b )$$

Evaluate

$$-32b^{2}a^{4}$$

Solution Steps

Combine \frac{b}{3} and -3b to get -\frac{8}{3}b.

$$-9a^{3}\left(\left(-a\right)b-\frac{ab}{3}\right)\left(-\frac{8}{3}\right)b$$

Multiply -9 and -\frac{8}{3} to get 24.

$$24a^{3}\left(\left(-a\right)b-\frac{ab}{3}\right)b$$

Use the distributive property to multiply 24a^{3} by \left(-a\right)b-\frac{ab}{3}.

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

Cancel out 3, the greatest common factor in 24 and 3.

$$\left(24a^{3}\left(-a\right)b-8aba^{3}\right)b$$

Use the distributive property to multiply 24a^{3}\left(-a\right)b-8aba^{3} by b.

$$24a^{3}\left(-a\right)b^{2}-8a^{4}b^{2}$$

Multiply 24 and -1 to get -24.

$$-24a^{3}ab^{2}-8a^{4}b^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-24a^{4}b^{2}-8a^{4}b^{2}$$

Combine -24a^{4}b^{2} and -8a^{4}b^{2} to get -32a^{4}b^{2}.

$$-32a^{4}b^{2}$$

Expand

$$-32b^{2}a^{4}$$

Solution Steps

Combine \frac{b}{3} and -3b to get -\frac{8}{3}b.

$$-9a^{3}\left(\left(-a\right)b-\frac{ab}{3}\right)\left(-\frac{8}{3}\right)b$$

Multiply -9 and -\frac{8}{3} to get 24.

$$24a^{3}\left(\left(-a\right)b-\frac{ab}{3}\right)b$$

Use the distributive property to multiply 24a^{3} by \left(-a\right)b-\frac{ab}{3}.

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

Cancel out 3, the greatest common factor in 24 and 3.

$$\left(24a^{3}\left(-a\right)b-8aba^{3}\right)b$$

Use the distributive property to multiply 24a^{3}\left(-a\right)b-8aba^{3} by b.

$$24a^{3}\left(-a\right)b^{2}-8a^{4}b^{2}$$

Multiply 24 and -1 to get -24.

$$-24a^{3}ab^{2}-8a^{4}b^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-24a^{4}b^{2}-8a^{4}b^{2}$$

Combine -24a^{4}b^{2} and -8a^{4}b^{2} to get -32a^{4}b^{2}.

$$-32a^{4}b^{2}$$