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25\left(x^{7}\right)^{2}+10x^{7}+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x^{7}+1\right)^{2}.
25x^{14}+10x^{7}+1
To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.
25\left(x^{7}\right)^{2}+10x^{7}+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x^{7}+1\right)^{2}.
25x^{14}+10x^{7}+1
To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.