Giải thích các bước giải:

$\begin{aligned}
& \text{a) Ta có:} \\
& \text{VT} = (x - y)(x^{n-1} + x^{n-2}y + \dots + xy^{n-2} + y^{n-1}) \\
& \text{VT} = x(x^{n-1} + x^{n-2}y + \dots + xy^{n-2} + y^{n-1}) - y(x^{n-1} + x^{n-2}y + \dots + xy^{n-2} + y^{n-1}) \\
& \text{VT} = (x^n + x^{n-1}y + \dots + x^2y^{n-2} + xy^{n-1}) - (x^{n-1}y + x^{n-2}y^2 + \dots + xy^{n-1} + y^n) \\
& \text{VT} = x^n + (x^{n-1}y - x^{n-1}y) + (x^{n-2}y^2 - x^{n-2}y^2) + \dots + (xy^{n-1} - xy^{n-1}) - y^n \\
& \text{VT} = x^n - y^n \\
& \text{VT} = \text{VP (điều phải chứng minh)} \\
& \\
& \text{b) Ta có:} \\
& \text{VT} = (x + y)(x^{2n} - x^{2n-1}y + x^{2n-2}y^2 - \dots - xy^{2n-1} + y^{2n}) \\
& \text{VT} = x(x^{2n} - x^{2n-1}y + x^{2n-2}y^2 - \dots - xy^{2n-1} + y^{2n}) + y(x^{2n} - x^{2n-1}y + x^{2n-2}y^2 - \dots - xy^{2n-1} + y^{2n}) \\
& \text{VT} = (x^{2n+1} - x^{2n}y + x^{2n-1}y^2 - \dots - x^2y^{2n-1} + xy^{2n}) + (x^{2n}y - x^{2n-1}y^2 + x^{2n-2}y^3 - \dots - xy^{2n} + y^{2n+1}) \\
& \text{VT} = x^{2n+1} + (-x^{2n}y + x^{2n}y) + (x^{2n-1}y^2 - x^{2n-1}y^2) + \dots + (xy^{2n} - xy^{2n}) + y^{2n+1} \\
& \text{VT} = x^{2n+1} + y^{2n+1} \\
& \text{VT} = \text{VP (điều phải chứng minh)} \\
\end{aligned}$