Solve (x^3+2)^3

$$( x ^ { 3 } + 2 ) ^ { 3 }$$

Expand

$$x^{9}+6x^{6}+12x^{3}+8$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$x^{9}+6\left(x^{3}\right)^{2}+12x^{3}+8$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{9}+6x^{6}+12x^{3}+8$$

Evaluate

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

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$x^{9}+6\left(x^{3}\right)^{2}+12x^{3}+8$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{9}+6x^{6}+12x^{3}+8$$