Solve left(-3a^2bright)^3-left(2a^3right)^2{left(-bright)}^3+3{a}^6{b}^3

$${ \left(-3 { a }^{ 2 } b \right) }^{ 3 } - { \left(2 { a }^{ 3 } \right) }^{ 2 } { \left(-b \right) }^{ 3 } +3 { a }^{ 6 } { b }^{ 3 }$$

Evaluate

$$-20b^{3}a^{6}$$

Solution Steps

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

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}b^{3}-\left(2a^{3}\right)^{2}\left(-b\right)^{3}+3a^{6}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(-3\right)^{3}a^{6}b^{3}-\left(2a^{3}\right)^{2}\left(-b\right)^{3}+3a^{6}b^{3}$$

Calculate -3 to the power of 3 and get -27.

$$-27a^{6}b^{3}-\left(2a^{3}\right)^{2}\left(-b\right)^{3}+3a^{6}b^{3}$$

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

$$-27a^{6}b^{3}-2^{2}\left(a^{3}\right)^{2}\left(-b\right)^{3}+3a^{6}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$-27a^{6}b^{3}-2^{2}a^{6}\left(-b\right)^{3}+3a^{6}b^{3}$$

Calculate 2 to the power of 2 and get 4.

$$-27a^{6}b^{3}-4a^{6}\left(-b\right)^{3}+3a^{6}b^{3}$$

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

$$-27a^{6}b^{3}-4a^{6}\left(-1\right)^{3}b^{3}+3a^{6}b^{3}$$

Calculate -1 to the power of 3 and get -1.

$$-27a^{6}b^{3}-4a^{6}\left(-1\right)b^{3}+3a^{6}b^{3}$$

Multiply -4 and -1 to get 4.

$$-27a^{6}b^{3}+4a^{6}b^{3}+3a^{6}b^{3}$$

Combine -27a^{6}b^{3} and 4a^{6}b^{3} to get -23a^{6}b^{3}.

$$-23a^{6}b^{3}+3a^{6}b^{3}$$

Combine -23a^{6}b^{3} and 3a^{6}b^{3} to get -20a^{6}b^{3}.

$$-20a^{6}b^{3}$$

Expand

$$-20b^{3}a^{6}$$

Solution Steps

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

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}b^{3}-\left(2a^{3}\right)^{2}\left(-b\right)^{3}+3a^{6}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(-3\right)^{3}a^{6}b^{3}-\left(2a^{3}\right)^{2}\left(-b\right)^{3}+3a^{6}b^{3}$$

Calculate -3 to the power of 3 and get -27.

$$-27a^{6}b^{3}-\left(2a^{3}\right)^{2}\left(-b\right)^{3}+3a^{6}b^{3}$$

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

$$-27a^{6}b^{3}-2^{2}\left(a^{3}\right)^{2}\left(-b\right)^{3}+3a^{6}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$-27a^{6}b^{3}-2^{2}a^{6}\left(-b\right)^{3}+3a^{6}b^{3}$$

Calculate 2 to the power of 2 and get 4.

$$-27a^{6}b^{3}-4a^{6}\left(-b\right)^{3}+3a^{6}b^{3}$$

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

$$-27a^{6}b^{3}-4a^{6}\left(-1\right)^{3}b^{3}+3a^{6}b^{3}$$

Calculate -1 to the power of 3 and get -1.

$$-27a^{6}b^{3}-4a^{6}\left(-1\right)b^{3}+3a^{6}b^{3}$$

Multiply -4 and -1 to get 4.

$$-27a^{6}b^{3}+4a^{6}b^{3}+3a^{6}b^{3}$$

Combine -27a^{6}b^{3} and 4a^{6}b^{3} to get -23a^{6}b^{3}.

$$-23a^{6}b^{3}+3a^{6}b^{3}$$

Combine -23a^{6}b^{3} and 3a^{6}b^{3} to get -20a^{6}b^{3}.

$$-20a^{6}b^{3}$$