Solve ({left(sqrt{x+x}right)}^2-x*left(x^2right)^2

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

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

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

Combine x and x to get 2x.

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

Calculate \sqrt{2x} to the power of 2 and get 2x.

$$2x-x^{5}$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$-x^{5}+2x$$

Factor out x. Polynomial -x^{4}+2 is not factored since it does not have any rational roots.

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