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

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

Evaluate

$$3ba^{4}$$

Solution Steps

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

$$\left(-\frac{3}{2}a^{3}b+ab\left(5a^{2}-\left(-a^{2}\right)\right)\right)\left(-\frac{2}{3}\right)a-b\left(-8a^{4}+2a^{4}\right)$$

Use the distributive property to multiply -\frac{3}{2}a^{3}b+ab\left(5a^{2}-\left(-a^{2}\right)\right) by -\frac{2}{3}.

$$\left(a^{3}b-\frac{2}{3}ab\left(5a^{2}-\left(-a^{2}\right)\right)\right)a-b\left(-8a^{4}+2a^{4}\right)$$

Use the distributive property to multiply a^{3}b-\frac{2}{3}ab\left(5a^{2}-\left(-a^{2}\right)\right) by a.

$$ba^{4}-\frac{2}{3}b\left(5a^{2}-\left(-a^{2}\right)\right)a^{2}-b\left(-8a^{4}+2a^{4}\right)$$

Combine -8a^{4} and 2a^{4} to get -6a^{4}.

$$ba^{4}-\frac{2}{3}b\left(5a^{2}-\left(-a^{2}\right)\right)a^{2}-b\left(-6\right)a^{4}$$

Combine ba^{4} and -b\left(-6\right)a^{4} to get 7ba^{4}.

$$7ba^{4}-\frac{2}{3}b\left(5a^{2}-\left(-a^{2}\right)\right)a^{2}$$

Multiply -1 and -1 to get 1.

$$7ba^{4}-\frac{2}{3}b\left(5a^{2}+a^{2}\right)a^{2}$$

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

$$7ba^{4}-\frac{2}{3}b\times 6a^{2}a^{2}$$

Multiply -\frac{2}{3} and 6 to get -4.

$$7ba^{4}-4ba^{2}a^{2}$$

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

$$7ba^{4}-4ba^{4}$$

Combine 7ba^{4} and -4ba^{4} to get 3ba^{4}.

$$3ba^{4}$$

Expand

$$3ba^{4}$$

Solution Steps

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

$$\left(-\frac{3}{2}a^{3}b+ab\left(5a^{2}-\left(-a^{2}\right)\right)\right)\left(-\frac{2}{3}\right)a-b\left(-8a^{4}+2a^{4}\right)$$

Use the distributive property to multiply -\frac{3}{2}a^{3}b+ab\left(5a^{2}-\left(-a^{2}\right)\right) by -\frac{2}{3}.

$$\left(a^{3}b-\frac{2}{3}ab\left(5a^{2}-\left(-a^{2}\right)\right)\right)a-b\left(-8a^{4}+2a^{4}\right)$$

Use the distributive property to multiply a^{3}b-\frac{2}{3}ab\left(5a^{2}-\left(-a^{2}\right)\right) by a.

$$ba^{4}-\frac{2}{3}b\left(5a^{2}-\left(-a^{2}\right)\right)a^{2}-b\left(-8a^{4}+2a^{4}\right)$$

Combine -8a^{4} and 2a^{4} to get -6a^{4}.

$$ba^{4}-\frac{2}{3}b\left(5a^{2}-\left(-a^{2}\right)\right)a^{2}-b\left(-6\right)a^{4}$$

Combine ba^{4} and -b\left(-6\right)a^{4} to get 7ba^{4}.

$$7ba^{4}-\frac{2}{3}b\left(5a^{2}-\left(-a^{2}\right)\right)a^{2}$$

Multiply -1 and -1 to get 1.

$$7ba^{4}-\frac{2}{3}b\left(5a^{2}+a^{2}\right)a^{2}$$

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

$$7ba^{4}-\frac{2}{3}b\times 6a^{2}a^{2}$$

Multiply -\frac{2}{3} and 6 to get -4.

$$7ba^{4}-4ba^{2}a^{2}$$

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

$$7ba^{4}-4ba^{4}$$

Combine 7ba^{4} and -4ba^{4} to get 3ba^{4}.

$$3ba^{4}$$