From 790299f57a528a7541f53c3bd85ab8a9387877dd Mon Sep 17 00:00:00 2001
From: HombreLaser <sebastian-440@live.com>
Date: Thu, 11 Jan 2024 11:11:20 -0600
Subject: Commit inicial

---
 main.tex | 84 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 84 insertions(+)
 create mode 100644 main.tex

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
new file mode 100644
index 0000000..bbd7fb6
--- /dev/null
+++ b/main.tex
@@ -0,0 +1,84 @@
+\documentclass{article}
+\usepackage{graphicx} % Required for inserting images
+
+\title{Laboratorio}
+\author{Alexx}
+\date{January 2024}
+
+\begin{document}
+
+\maketitle
+
+\textbf{Encuentre el término de orden $r=4$ $(x+4)^4$}
+
+\[
+\frac{n(n-1)\ldots(n-r+2)}{(r-1)!}a^{n-r+1}b^{r-1}
+\]
+
+\[
+= \frac{4(4-1)(4-2)}{(4-1)!}x^{4-4+1}(4^{4-1})
+\]
+
+\[
+= \frac{4(3)(2)}{(3)!}x^{4-4+1}(4^{4-1})
+\]
+
+\[
+= \frac{24}{(3)!}x^{4-4+1}(4^{4-1})
+\]
+
+\[
+= \frac{24}{6}x^{4-4+1}(4^{4-1})
+\]
+
+\[
+= 4x^{4-4+1}(4^{4-1}) = (4x^{1})(4^{3}) = 256x
+\]
+
+\textbf{Desarrolle $(3x+5)^4$}
+
+\[
+(3x+5)^4
+\]
+
+\[
+= 81x^4+4(3x)^{4-1}(5)+\frac{4(4-1)}{2!}(3x)^{4-2}(5^2)+\frac{4(4-1)(4-2)}{3!}(3x)^{4-3}(5^3)+5^4
+\]
+
+\[
+= 81x^4+4(27x)^{3}(5)+\frac{4(4-1)}{2!}(3x)^{4-2}(5^2)+\frac{4(4-1)(4-2)}{3!}(3x)^{4-3}(5^3)+5^4
+\]
+
+\[
+= 81x^4+540x^3+\frac{4(3)}{2}(3x)^{4-2}(5^2)+\frac{4(4-1)(4-2)}{3!}(3x)^{4-3}(5^3)+5^4
+\]
+
+\[
+= 81x^4+540x^3+(6)(9x^2)(5^2)+\frac{4(4-1)(4-2)}{3!}(3x)^{4-3}(5^3)+5^4
+\]
+
+\[
+= 81x^4+540x^3+1,350x^2+\frac{4(3)(2)}{6}(3x)^{4-3}(5^3)+5^4
+\]
+
+\[
+= 81x^4+540x^3+1,350x^2+(4)(3x)^{4-3}(9)+5^4
+\]
+
+\[
+= 81x^4+540x^3+1,350x^2+(12x)(5^3)+5^4
+\]
+
+\[
+= 81x^4+540x^3+1,350x^2+(12x)(125)+5^4
+\]
+
+\[
+= 81x^4+540x^3+1,350x^2+1500x+5^4
+\]
+
+\[
+= 81x^4+540x^3+1,350x^2+1500x+625
+\]
+
+\end{document}
-- 
cgit v1.2.3

