[tex](x+1)^4+(x+1)^2+1= \\ \\ \boxed{(a+b)^2=a^2+2ab+b^2} \\ \boxed{(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4} \\ \\ (x+1)^4=x^4+4x^{3}1+6x^{2}1^{2}+4x1^3+1^4 \\ \\=x^4+4x^3 +6x^2+4x+1 \\ \\ (x+1)^2=x^2+2x1+1^2 \\ \\ = x^2+2x+1 \\ \\ x^4+4x^3 +6x^2+4x+1 + x^2+2x+1 +1 = \\ \\ = x^4+4x^3+7x^2+6x+3 \\ \\ \text{Final}[/tex]
