Pascal's Triangle

Binomial expansion

${\begin{aligned}(a+b)^{0}&=1\\(a+b)^{1}&=a+b\\(a+b)^{2}&=a^{2}+2ab+b^{2}\\(a+b)^{3}&=(a+b)(a+b)^{2}=(a+b)(a^{2}+2ab+b^{2})\\&=a^{3}+2a^{2}b+ab^{2}+ba^{2}+2ab^{2}+b^{3}\\&=a^{3}+3a^{2}b+3ab^{2}+b^{3}\\(a+b)^{4}&=\cdots \end{aligned}}$

Pascal's triangle

Failed to parse (unknown function "\begin{tabular}"): {\displaystyle \begin{tabular}{rccccccccc} $n=0$:& & & & & 1\\\noalign{\smallskip\smallskip} $n=1$:& & & & 1 & & 1\\\noalign{\smallskip\smallskip} $n=2$:& & & 1 & & 2 & & 1\\\noalign{\smallskip\smallskip} $n=3$:& & 1 & & 3 & & 3 & & 1\\\noalign{\smallskip\smallskip} $n=4$:& 1 & & 4 & & 6 & & 4 & & 1\\\noalign{\smallskip\smallskip} \end{tabular} }