(i) Expand \((1+x)^4\), simplifying all coefficients.

(ii) Expand \((6-x)^4\), simplifying all coefficients.

(iii) Hence express \((6-x)^4-(1+x)^4=175\) in the form \(ax^3+bx^2+cx+d=0\), where \(a\), \(b\), \(c\), and \(d\) are integers.

(iv) Show that \(x=2\) is a solution of the equation in part (iii) and show that this equation has no other real roots.