Solve f(x)=(x^6+4)^3

$$f ( x ) = ( x ^ { 6 } + 4 ) ^ { 3 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x^{6}+4\right)^{3}.

$$\left(x^{6}\right)^{3}+12\left(x^{6}\right)^{2}+48x^{6}+64$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$x^{18}+12\left(x^{6}\right)^{2}+48x^{6}+64$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$x^{18}+12x^{12}+48x^{6}+64$$

Expand

$$x^{18}+12x^{12}+48x^{6}+64$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x^{6}+4\right)^{3}.

$$\left(x^{6}\right)^{3}+12\left(x^{6}\right)^{2}+48x^{6}+64$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$x^{18}+12\left(x^{6}\right)^{2}+48x^{6}+64$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$x^{18}+12x^{12}+48x^{6}+64$$