Solve f(x)=(4x^6+2)^3

$$f ( x ) = ( 4 x ^ { 6 } + 2 ) ^ { 3 }$$

Evaluate

$$8\left(2x^{6}+1\right)^{3}$$

Solution Steps

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

$$64\left(x^{6}\right)^{3}+96\left(x^{6}\right)^{2}+48x^{6}+8$$

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

$$64x^{18}+96\left(x^{6}\right)^{2}+48x^{6}+8$$

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

$$64x^{18}+96x^{12}+48x^{6}+8$$

Expand

$$64x^{18}+96x^{12}+48x^{6}+8$$

Solution Steps

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

$$64\left(x^{6}\right)^{3}+96\left(x^{6}\right)^{2}+48x^{6}+8$$

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

$$64x^{18}+96\left(x^{6}\right)^{2}+48x^{6}+8$$

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

$$64x^{18}+96x^{12}+48x^{6}+8$$