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authorHombreLaser <sebastian-440@live.com>2024-01-11 11:11:20 -0600
committerHombreLaser <sebastian-440@live.com>2024-01-11 11:11:20 -0600
commit790299f57a528a7541f53c3bd85ab8a9387877dd (patch)
tree44bc609abf3715fff9809dd5b5bd81fb6d67c82a
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+\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}