Solve 2ab^3+2a^3left(-bright)^3-frac{4a^2{b}^3}{a}--2{a}^3{b}^3

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

Evaluate

$$-2ab^{3}$$

Solution Steps

Cancel out a in both numerator and denominator.

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

The opposite of -2a^{3}b^{3} is 2a^{3}b^{3}.

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

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

$$2ab^{3}+2a^{3}\left(-1\right)^{3}b^{3}-4ab^{3}+2a^{3}b^{3}$$

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

$$2ab^{3}+2a^{3}\left(-1\right)b^{3}-4ab^{3}+2a^{3}b^{3}$$

Multiply 2 and -1 to get -2.

$$2ab^{3}-2a^{3}b^{3}-4ab^{3}+2a^{3}b^{3}$$

Combine 2ab^{3} and -4ab^{3} to get -2ab^{3}.

$$-2ab^{3}-2a^{3}b^{3}+2a^{3}b^{3}$$

Combine -2a^{3}b^{3} and 2a^{3}b^{3} to get 0.

$$-2ab^{3}$$

Expand

$$-2ab^{3}$$

Solution Steps

Cancel out a in both numerator and denominator.

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

The opposite of -2a^{3}b^{3} is 2a^{3}b^{3}.

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

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

$$2ab^{3}+2a^{3}\left(-1\right)^{3}b^{3}-4ab^{3}+2a^{3}b^{3}$$

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

$$2ab^{3}+2a^{3}\left(-1\right)b^{3}-4ab^{3}+2a^{3}b^{3}$$

Multiply 2 and -1 to get -2.

$$2ab^{3}-2a^{3}b^{3}-4ab^{3}+2a^{3}b^{3}$$

Combine 2ab^{3} and -4ab^{3} to get -2ab^{3}.

$$-2ab^{3}-2a^{3}b^{3}+2a^{3}b^{3}$$

Combine -2a^{3}b^{3} and 2a^{3}b^{3} to get 0.

$$-2ab^{3}$$