Solve 3a(2a^2+1)-2a^2(3a-1)-10/3a^2(3/5+9a)-(-2a)^3-3a

$$3 a ( 2 a ^ { 2 } + 1 ) - 2 a ^ { 2 } ( 3 a - 1 ) - \frac { 10 } { 3 } a ^ { 2 } ( \frac { 3 } { 5 } + 9 a ) - ( - 2 a ) ^ { 3 } - 3 a$$

Evaluate

$$-22a^{3}$$

Solution Steps

Use the distributive property to multiply 3a by 2a^{2}+1.

$$6a^{3}+3a-2a^{2}\left(3a-1\right)-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)-\left(-2a\right)^{3}-3a$$

Expand \left(-2a\right)^{3}.

$$6a^{3}+3a-2a^{2}\left(3a-1\right)-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)-\left(-2\right)^{3}a^{3}-3a$$

Calculate -2 to the power of 3 and get -8.

$$6a^{3}+3a-2a^{2}\left(3a-1\right)-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)-\left(-8a^{3}\right)-3a$$

The opposite of -8a^{3} is 8a^{3}.

$$6a^{3}+3a-2a^{2}\left(3a-1\right)-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)+8a^{3}-3a$$

Use the distributive property to multiply -2a^{2} by 3a-1.

$$6a^{3}+3a-6a^{3}+2a^{2}-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)+8a^{3}-3a$$

Combine 6a^{3} and -6a^{3} to get 0.

$$3a+2a^{2}-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)+8a^{3}-3a$$

Use the distributive property to multiply -\frac{10}{3}a^{2} by \frac{3}{5}+9a.

$$3a+2a^{2}-2a^{2}-30a^{3}+8a^{3}-3a$$

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

$$3a-30a^{3}+8a^{3}-3a$$

Combine -30a^{3} and 8a^{3} to get -22a^{3}.

$$3a-22a^{3}-3a$$

Combine 3a and -3a to get 0.

$$-22a^{3}$$

Expand

$$-22a^{3}$$

Solution Steps

Use the distributive property to multiply 3a by 2a^{2}+1.

$$6a^{3}+3a-2a^{2}\left(3a-1\right)-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)-\left(-2a\right)^{3}-3a$$

Expand \left(-2a\right)^{3}.

$$6a^{3}+3a-2a^{2}\left(3a-1\right)-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)-\left(-2\right)^{3}a^{3}-3a$$

Calculate -2 to the power of 3 and get -8.

$$6a^{3}+3a-2a^{2}\left(3a-1\right)-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)-\left(-8a^{3}\right)-3a$$

The opposite of -8a^{3} is 8a^{3}.

$$6a^{3}+3a-2a^{2}\left(3a-1\right)-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)+8a^{3}-3a$$

Use the distributive property to multiply -2a^{2} by 3a-1.

$$6a^{3}+3a-6a^{3}+2a^{2}-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)+8a^{3}-3a$$

Combine 6a^{3} and -6a^{3} to get 0.

$$3a+2a^{2}-\frac{10}{3}a^{2}\left(\frac{3}{5}+9a\right)+8a^{3}-3a$$

Use the distributive property to multiply -\frac{10}{3}a^{2} by \frac{3}{5}+9a.

$$3a+2a^{2}-2a^{2}-30a^{3}+8a^{3}-3a$$

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

$$3a-30a^{3}+8a^{3}-3a$$

Combine -30a^{3} and 8a^{3} to get -22a^{3}.

$$3a-22a^{3}-3a$$

Combine 3a and -3a to get 0.

$$-22a^{3}$$