Solve (-a^{2})^{3}+(-a^3)^2-a^2-a^3

$$( - a ^ { 2 } ) ^ { 3 } + ( - a ^ { 3 } ) ^ { 2 } - a ^ { 2 } - a ^ { 3 }$$

Evaluate

$$-\left(a+1\right)a^{2}$$

Solution Steps

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

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

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

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

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

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

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

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

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

$$-a^{6}+a^{6}-a^{2}-a^{3}$$

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

$$-a^{2}-a^{3}$$

Expand

$$-a^{3}-a^{2}$$

Solution Steps

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

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

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

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

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

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

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

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

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

$$-a^{6}+a^{6}-a^{2}-a^{3}$$

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

$$-a^{2}-a^{3}$$