Solve (3x^6+9)^2

$$( 3 x ^ { 6 } + 9 ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x^{6}+9\right)^{2}.

$$9\left(x^{6}\right)^{2}+54x^{6}+81$$

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

$$9x^{12}+54x^{6}+81$$

Expand

$$9x^{12}+54x^{6}+81$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x^{6}+9\right)^{2}.

$$9\left(x^{6}\right)^{2}+54x^{6}+81$$

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

$$9x^{12}+54x^{6}+81$$