Solve x^6*(-x)^3-(-x)^2*(-x)^7

$$x ^ { 6 } \cdot ( - x ) ^ { 3 } - ( - x ) ^ { 2 } \cdot ( - x ) ^ { 7 }$$

Evaluate

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Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$x^{6}\left(-x\right)^{3}-\left(-x\right)^{9}$$

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

$$x^{6}\left(-1\right)^{3}x^{3}-\left(-x\right)^{9}$$

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

$$x^{6}\left(-1\right)x^{3}-\left(-x\right)^{9}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$x^{9}\left(-1\right)-\left(-x\right)^{9}$$

Expand \left(-x\right)^{9}.

$$x^{9}\left(-1\right)-\left(-1\right)^{9}x^{9}$$

Calculate -1 to the power of 9 and get -1.

$$x^{9}\left(-1\right)-\left(-x^{9}\right)$$

Multiply -1 and -1 to get 1.

$$x^{9}\left(-1\right)+x^{9}$$

Combine x^{9}\left(-1\right) and x^{9} to get 0.

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Factor

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Solution Steps

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

$$\left(-x\right)^{2}\left(-x^{7}-\left(-x\right)^{7}\right)$$

Consider -x^{7}-\left(-x\right)^{7}. Simplify.

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