Solve (-a)^3*a^2-(-a)^2*(-a)^3

$$( - a ) ^ { 3 } \cdot a ^ { 2 } - ( - a ) ^ { 2 } \cdot ( - a ) ^ { 3 }$$

Evaluate

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Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(-a\right)^{3}a^{2}-\left(-a\right)^{5}$$

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

$$\left(-1\right)^{3}a^{3}a^{2}-\left(-a\right)^{5}$$

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

$$-a^{3}a^{2}-\left(-a\right)^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-a^{5}-\left(-a\right)^{5}$$

Expand \left(-a\right)^{5}.

$$-a^{5}-\left(-1\right)^{5}a^{5}$$

Calculate -1 to the power of 5 and get -1.

$$-a^{5}-\left(-a^{5}\right)$$

Multiply -1 and -1 to get 1.

$$-a^{5}+a^{5}$$

Combine -a^{5} and a^{5} to get 0.

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Factor

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Solution Steps

Factor out common term \left(-a\right)^{2} by using distributive property.

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

Consider -a^{3}-\left(-a\right)^{3}. Simplify.

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