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81\left(x^{8}\right)^{2}+54x^{8}+9
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9x^{8}+3\right)^{2}.
81x^{16}+54x^{8}+9
To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.
81\left(x^{8}\right)^{2}+54x^{8}+9
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9x^{8}+3\right)^{2}.
81x^{16}+54x^{8}+9
To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.