Solve 3a^{3}(-1/2b)+ab[5a^2-(-a^2)]}(-2/3a)-b(-8a^4+2a^4)

$$3 a ^ { 3 } ( - \frac { 1 } { 2 } b ) + a b [ 5 a ^ { 2 } - ( - a ^ { 2 } ) ] \} ( - \frac { 2 } { 3 } a ) - b ( - 8 a ^ { 4 } + 2 a ^ { 4 } )$$

Evaluate

$$\frac{9ba^{3}}{2}$$

Solution Steps

Multiply 3 and -\frac{1}{2} to get -\frac{3}{2}.

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

Multiply -1 and -1 to get 1.

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

Combine 5a^{2} and a^{2} to get 6a^{2}.

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

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

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

Combine -\frac{3}{2}a^{3}b and a^{3}b\times 6 to get \frac{9}{2}a^{3}b.

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

Expand

$$\frac{9ba^{3}}{2}$$

Solution Steps

Multiply 3 and -\frac{1}{2} to get -\frac{3}{2}.

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

Multiply -1 and -1 to get 1.

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

Combine 5a^{2} and a^{2} to get 6a^{2}.

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

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

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

Combine -\frac{3}{2}a^{3}b and a^{3}b\times 6 to get \frac{9}{2}a^{3}b.

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