$\displaystyle \mbox{a) }\, (a\, +\, b)^2\, =\, (a\, +\, b)(a\, +\, b)\, =\, (a\, +\, b)a\, +\, (a\, +\, b)b$
$\displaystyle =\, a^2\, +\, ba\, +\, ab\, + \, b^2\, =\, a\, +\, ba\, +\, ab\, +\, b\, =\, (a\, +\, b)$
Subtract $\displaystyle (a\, +\, b)$ from either side. See if that leads anywhere helpful...?
$\displaystyle \mbox{b) }\, (ab)^2\, =\, (ab)(ab)\, =\, abab\, =\, a^2 b^2$
$\displaystyle a^{-1}ababb^{-1}\, =\, a^{-1}a^2 b^2 b^{-1}$
$\displaystyle ebae\, =\, eabe$
...where $\displaystyle e$ is the group's identity element. The result follows immediately.