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We need to simplify the expression:
[tex]\mleft(x+\frac{6}{7}\mright)^2[/tex]We can use the following identity:
[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]In this problem, we have:
[tex]\begin{gathered} a=x \\ \\ b=\frac{6}{7} \end{gathered}[/tex]Thus, we obtain:
[tex]\begin{gathered} \mleft(x+\frac{6}{7}\mright)^2=x^2+2\cdot x\cdot\frac{6}{7}+\mleft(\frac{6}{7}\mright)^2 \\ \\ \mleft(x+\frac{6}{7}\mright)^2=x^{2}+\frac{12}{7}x+\frac{36}{49} \end{gathered}[/tex]Therefore, after simplifying, we obtain:
[tex]x^2+\frac{12}{7}x+\frac{36}{49}[/tex]