Binomial Theorem with Examples

Binomial Theorem: [katex]\boxed{(a+b)^n=\begin{pmatrix}n\\0\end{pmatrix}a^nb^0+\begin{pmatrix}n\\1\end{pmatrix}a^{n-1}b^1+\begin{pmatrix}n\\2\end{pmatrix}a^{n-2}b^2+\begin{pmatrix}n\\3\end{pmatrix}a^{n-4}b^4+……..\begin{pmatrix}n\\n-1\end{pmatrix}a^1b^{n-1}+\begin{pmatrix}n\\n\end{pmatrix}a^0b^n}[/katex] where [katex]a[/katex] and [katex]b[/katex] are real numbers and [katex]n\geq1[/katex] [katex]\begin{pmatrix}n\\0\end{pmatrix},\begin{pmatrix}n\\1\end{pmatrix},\begin{pmatrix}n\\2\end{pmatrix},……….,\begin{pmatrix}n\\n\end{pmatrix}[/katex] are binomial cofficient. [katex]a[/katex] and [katex]b[/katex] are exponents and […]