2.4: Binomial expansions and cubic equation

Expand $(1 + x)^{4}$, simplifying all coefficients.

Expand $(6 - x)^{4}$, simplifying all coefficients.

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.

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