Solve (3x^4+1)^3

$$( 3 x ^ { 4 } + 1 ) ^ { 3 }$$

Expand

$$27x^{12}+27x^{8}+9x^{4}+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(3x^{4}+1\right)^{3}.

$$27\left(x^{4}\right)^{3}+27\left(x^{4}\right)^{2}+9x^{4}+1$$

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

$$27x^{12}+27\left(x^{4}\right)^{2}+9x^{4}+1$$

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

$$27x^{12}+27x^{8}+9x^{4}+1$$

Evaluate

$$\left(3x^{4}+1\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(3x^{4}+1\right)^{3}.

$$27\left(x^{4}\right)^{3}+27\left(x^{4}\right)^{2}+9x^{4}+1$$

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

$$27x^{12}+27\left(x^{4}\right)^{2}+9x^{4}+1$$

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

$$27x^{12}+27x^{8}+9x^{4}+1$$