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

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

Evaluate

$$2x^{5}$$

Solution Steps

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

$$\left(-x\right)^{5}+2x\left(-x\right)^{4}-\left(-x\right)x^{4}$$

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

$$\left(-1\right)^{5}x^{5}+2x\left(-x\right)^{4}-\left(-xx^{4}\right)$$

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

$$-x^{5}+2x\left(-x\right)^{4}-\left(-xx^{4}\right)$$

Expand \left(-x\right)^{4}.

$$-x^{5}+2x\left(-1\right)^{4}x^{4}-\left(-xx^{4}\right)$$

Calculate -1 to the power of 4 and get 1.

$$-x^{5}+2x\times 1x^{4}-\left(-xx^{4}\right)$$

Multiply 2 and 1 to get 2.

$$-x^{5}+2xx^{4}-\left(-xx^{4}\right)$$

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

$$-x^{5}+2x^{5}-\left(-xx^{4}\right)$$

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

$$x^{5}-\left(-xx^{4}\right)$$

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

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

Multiply -1 and -1 to get 1.

$$x^{5}+x^{5}$$

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

$$2x^{5}$$

Expand

$$2x^{5}$$

Solution Steps

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

$$\left(-x\right)^{5}+2x\left(-x\right)^{4}-\left(-x\right)x^{4}$$

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

$$\left(-1\right)^{5}x^{5}+2x\left(-x\right)^{4}-\left(-xx^{4}\right)$$

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

$$-x^{5}+2x\left(-x\right)^{4}-\left(-xx^{4}\right)$$

Expand \left(-x\right)^{4}.

$$-x^{5}+2x\left(-1\right)^{4}x^{4}-\left(-xx^{4}\right)$$

Calculate -1 to the power of 4 and get 1.

$$-x^{5}+2x\times 1x^{4}-\left(-xx^{4}\right)$$

Multiply 2 and 1 to get 2.

$$-x^{5}+2xx^{4}-\left(-xx^{4}\right)$$

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

$$-x^{5}+2x^{5}-\left(-xx^{4}\right)$$

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

$$x^{5}-\left(-xx^{4}\right)$$

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

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

Multiply -1 and -1 to get 1.

$$x^{5}+x^{5}$$

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

$$2x^{5}$$