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

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

Evaluate

$$\left(x^{2}+3\right)x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$x^{4}+x^{6}+2\left(x^{2}\right)^{2}$$

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

$$x^{4}+x^{6}+2x^{4}$$

Combine x^{4} and 2x^{4} to get 3x^{4}.

$$3x^{4}+x^{6}$$

Factor

$$\left(x^{2}+3\right)x^{4}$$

Solution Steps

Factor out common term x^{4} by using distributive property.

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

Consider 1+x^{2}+2. Simplify.

$$x^{2}+3$$

Rewrite the complete factored expression. Polynomial x^{2}+3 is not factored since it does not have any rational roots.

$$x^{4}\left(x^{2}+3\right)$$