Solve x^{3}*(-x^2)+2x^3*(-x)^2-x*x^4

$$x ^ { 3 } \cdot ( - x ^ { 2 } ) + 2 x ^ { 3 } \cdot ( - x ) ^ { 2 } - x \cdot x ^ { 4 }$$

Evaluate

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Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

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

Calculate -x to the power of 2 and get x^{2}.

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

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

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

Combine 2x^{5} and -x^{5} to get x^{5}.

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

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

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

Combine x^{5}\left(-1\right) and x^{5} to get 0.

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Factor

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Solution Steps

Factor out common term x by using distributive property.

$$x\left(-x^{4}+2x^{4}-x^{4}\right)$$

Consider -x^{4}+2x^{4}-x^{4}. Simplify.

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