Solve left(x^4+2right)^3

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

Expand

$$x^{12}+6x^{8}+12x^{4}+8$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x^{4}+2\right)^{3}.

$$\left(x^{4}\right)^{3}+6\left(x^{4}\right)^{2}+12x^{4}+8$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$x^{12}+6\left(x^{4}\right)^{2}+12x^{4}+8$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{12}+6x^{8}+12x^{4}+8$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x^{4}+2\right)^{3}.

$$\left(x^{4}\right)^{3}+6\left(x^{4}\right)^{2}+12x^{4}+8$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$x^{12}+6\left(x^{4}\right)^{2}+12x^{4}+8$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{12}+6x^{8}+12x^{4}+8$$