Solve x^2*(-x)^6+x^3*(-x)^5

$$x ^ { 2 } \cdot ( - x ) ^ { 6 } + x ^ { 3 } \cdot ( - x ) ^ { 5 }$$

Evaluate

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Solution Steps

Expand \left(-x\right)^{6}.

$$x^{2}\left(-1\right)^{6}x^{6}+x^{3}\left(-x\right)^{5}$$

Calculate -1 to the power of 6 and get 1.

$$x^{2}\times 1x^{6}+x^{3}\left(-x\right)^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$x^{8}\times 1+x^{3}\left(-x\right)^{5}$$

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

$$x^{8}\times 1+x^{3}\left(-1\right)^{5}x^{5}$$

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

$$x^{8}\times 1+x^{3}\left(-1\right)x^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$x^{8}\times 1+x^{8}\left(-1\right)$$

Combine x^{8}\times 1 and x^{8}\left(-1\right) to get 0.

$$0$$

Factor

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Solution Steps

Factor out common term x by using distributive property.

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

Consider x^{7}-x^{7}. Simplify.

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