Formularios de Algebra
Enviado por Brigith0904 • 7 de Septiembre de 2021 • Apuntes • 1.221 Palabras (5 Páginas) • 82 Visitas
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PROPIEDADES ARITMÉTICAS | |
ASOCIATIVA | 𝑎(𝑏𝑐) = (𝑎𝑏)𝑐 |
CONMUTATIVA | 𝑎 + 𝑏 = 𝑏 + 𝑎 𝑦 𝑎𝑏 = 𝑏𝑎 |
DISTRIBUTIVA | 𝑎(𝑏 + 𝑐) = 𝑎𝑏 + 𝑎𝑐 |
LEYES DE EXPONENTES | |
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𝑎0 = 1; 𝑎 ≠ 0 | 𝑎−𝑚 = 1 ; 𝑎 ≠ 0 𝑎𝑚 |
𝑎𝑚 ⋅ 𝑎𝑛 = 𝑎𝑚+𝑛 | 𝑎𝑚 = 𝑎𝑚−𝑛 𝑎𝑛 |
(𝑎𝑚)𝑛 = 𝑎𝑚⋅𝑛 = 𝑎𝑛⋅𝑚 = (𝑎𝑛)𝑚 | 𝑚 𝑎 𝑛 = 𝑛√𝑎𝑚 |
(𝑎𝑚 ⋅ 𝑏𝑛 ⋅ 𝑐𝑝)𝑥 = 𝑎𝑚𝑥 ⋅ 𝑏𝑛𝑥 ⋅ 𝑐𝑝𝑥 | |
𝑎𝑚 𝑥 𝑎𝑚⋅𝑥 ( 𝑏𝑛 ) = 𝑏𝑛⋅𝑥 | 𝑎 −𝑚 𝑏 𝑚 ( ) = ( ) 𝑏 𝑎 |
LEY DE SIGNOS | |
MULTIPLICACIÓN | DIVISIÓN |
(+) × (+) = (+) | (+) ÷ (+) = (+) |
(−) × (−) = (+) | (−) ÷ (−) = (+) |
(+) × (−) = (−) | (+) ÷ (−) = (−) |
(−) × (+) = (−) | (−) ÷ (+) = (−) |
EJEMPLOS DE OPERACIONES ARITMÉTICAS | |
𝑎𝑏 + 𝑎𝑐 = 𝑎(𝑏 + 𝑐) | 𝑎 𝑐 𝑎𝑑 − 𝑏𝑐 − = 𝑏 𝑑 𝑏𝑑 |
𝑏 𝑎𝑏 𝑎 ( ) = 𝑐 𝑐 | 𝑎 − 𝑏 𝑏 − 𝑎 = 𝑐 − 𝑑 𝑑 − 𝑐 |
𝑎 (𝑏) = 𝑎 𝑐 𝑏𝑐 | 𝑎 + 𝑏 𝑎 𝑏 = + 𝑐 𝑐 𝑐 |
𝑎 𝑎𝑐 𝑏 = 𝑏 (𝑐) | 𝑎𝑏 + 𝑎𝑐 = 𝑏 + 𝑐, 𝑎 ≠ 0 𝑎 |
𝑎 𝑐 𝑎𝑑 + 𝑏𝑐 + = 𝑏 𝑑 𝑏𝑑 | 𝑎 (𝑏) = 𝑎𝑑 (𝑐) 𝑏𝑐 𝑑 |
PRODUCTOS NOTABLES | |
(𝑎 + 𝑏)2 = 𝑎2 + 2𝑎𝑏 + 𝑏2 | (𝑎 − 𝑏)2 = 𝑎2 − 2𝑎𝑏 + 𝑏2 |
(𝑎 + 𝑏)3 = 𝑎3 + 3𝑎2𝑏 + 3𝑎𝑏2 + 𝑏3 | |
(𝑎 + 𝑏)3 = 𝑎3 + 𝑏3 + 3𝑎𝑏(𝑎 + 𝑏) | |
(𝑎 − 𝑏)3 = 𝑎3 − 3𝑎2𝑏 + 3𝑎𝑏2 − 𝑏3 | |
(𝑎 − 𝑏)3 = 𝑎3 − 𝑏3 − 3𝑎𝑏(𝑎 − 𝑏) | |
𝑎2 − 𝑏2 = (𝑎 + 𝑏)(𝑎 − 𝑏) | |
(𝑥 + 𝑎)(𝑥 + 𝑏) = 𝑥2 + (𝑎 + 𝑏)𝑥 + 𝑎𝑏 | |
(𝑎 + 𝑏)2 + (𝑎 − 𝑏)2 = 2(𝑎2 + 𝑏2) | |
(𝑎 + 𝑏)2 − (𝑎 − 𝑏)2 = 4𝑎𝑏 | |
(𝑎 + 𝑏)(𝑎2 − 𝑎𝑏 + 𝑏2) = 𝑎3 + 𝑏3 | |
(𝑎 − 𝑏)(𝑎2 + 𝑎𝑏 + 𝑏2) = 𝑎3 − 𝑏3 | |
(𝑎 + 𝑏 + 𝑐)2 = 𝑎2 + 𝑏2 + 𝑐2 + 2𝑎𝑏 + 2𝑏𝑐 + 2𝑎𝑐 | |
(𝑎2 + 𝑎𝑏 + 𝑏2)(𝑎2 − 𝑎𝑏 + 𝑏2) = 𝑎4 + 𝑎2𝑏2 + 𝑎4 | |
(𝑎 + 𝑏 + 𝑐)3 = 𝑎3 + 𝑏3 + 𝑐3 + 3(𝑎 + 𝑏)(𝑎 + 𝑐)(𝑏 + 𝑐) | |
ECUACIÓN CUADRÁTICA | |
2 −𝑏 ± √𝑏2 − 4𝑎𝑐 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0 → 𝑥 = 2𝑎 | |
FACTORIZACIÓN | |
𝑎2𝑚 + 2𝑎𝑚𝑏𝑛 + 𝑏2𝑛 = (𝑎𝑚 + 𝑏𝑛)2 | |
𝑎2𝑚 − 2𝑎𝑚𝑏𝑛 + 𝑏2𝑛 = (𝑎𝑚 − 𝑏𝑛)2 | |
𝑎2𝑚 − 𝑏2𝑛 = (𝑎𝑚 + 𝑏𝑛)(𝑎𝑚 − 𝑏𝑛) | |
𝑎3𝑚 + 𝑏3𝑛 = (𝑎𝑚 + 𝑏𝑛)(𝑎2𝑚 − 𝑎𝑚𝑏𝑛 + 𝑏2𝑛) | |
𝑎3𝑚 − 𝑏3𝑛 = (𝑎𝑚 − 𝑏𝑛)(𝑎2𝑚 + 𝑎𝑚𝑏𝑛 + 𝑏2𝑛) | |
𝑥2 + (𝑎 + 𝑏)𝑥 + 𝑎𝑏 = (𝑥 + 𝑎)(𝑥 + 𝑏) | |
𝑎𝑥2𝑚 + 𝑏𝑥𝑚𝑦𝑛 + 𝑐𝑦𝑛 = (𝑎1𝑥𝑚 + 𝑐1𝑦𝑛)(𝑎2𝑥𝑚 + 𝑐2𝑦𝑛) 𝑎1𝑥𝑚 𝑐1𝑦𝑛 ⇒ 𝑎2𝑐1𝑥𝑚𝑦𝑛 𝑎 𝑥𝑚 𝑐 𝑦𝑛 ⇒ 𝑎 𝑐 𝑥𝑚𝑦𝑛 (+) 2 2 1 2 𝑏𝑥𝑚𝑦𝑛 | |
CURSO DE ÁLGEBRA | |
Si quieres aprender un poco más de álgebra, dale un vistazo a nuestro curso gratuito en YouTube, con cientos de ejercicios resueltos. | |
RADICALES | |
𝑛 √𝑎 = 𝑏 ↔ 𝑎 = 𝑏𝑛 | 1 𝑛√𝑎 = 𝑎𝑛 |
𝑚 𝑛 𝑚𝑛 √ √𝑎 = √𝑎 | 𝑛√𝑎𝑏 = 𝑛√𝑎 ⋅ 𝑛√𝑏 |
𝑛 𝑎 𝑛√𝑎 √𝑏 = 𝑛√𝑏 | 𝑚 𝑎𝑥 𝑚√𝑎𝑥 √ = 𝑏𝑦 𝑚√𝑏𝑦 |
𝑛 √𝑎𝑛 = 𝑎, 𝑠𝑖 𝑛 𝑒𝑠 𝑖𝑚𝑝𝑎𝑟 | 𝑛 √𝑎𝑛 = |𝑎|, 𝑠𝑖 𝑛 𝑒𝑠 𝑝𝑎𝑟 |
DESIGUALDADES | |
𝑆𝑖 𝑎 < 𝑏 → 𝑎 + 𝑐 < 𝑏 + 𝑐 𝑦 𝑎 − 𝑐 < 𝑏 − 𝑐 | |
𝑆𝑖 𝑎 < 𝑏 𝑦 𝑐 > 0 → 𝑎𝑐 < 𝑏𝑐 𝑦 𝑎/𝑐 < 𝑏/𝑐 | |
𝑆𝑖 𝑎 < 𝑏 𝑦 𝑐 < 0 → 𝑎𝑐 > 𝑏𝑐 𝑦 𝑎/𝑐 > 𝑏/𝑐 |
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