# Algunos archivos de matematicas

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• Publicado : 29 de septiembre de 2010

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FACTORIZACION
1.1 simplificar y efectuar calculo con expresiones algebraicas como a+b2 factorizando expresiones algebraicas.
FACTORIZACION
Es descomponer un número por sus distintos factores primos.
a2+ab+ab+b2

A² ab

Ab b²

AA

+

B

Si el binomio es negativo el segundo término del TCP sería negativo
1)(a+b)²= (a)²+ 2 (a) (b)+(b)²= a² + 2 ab + b²
2) (x+y)²= (x)²+ 2 (x) (y) + (y)
= x² + xy + y²
3) (2a+3b)= (2a)²+ 2 (2a) (3b) + (3b)²
=4a²+12ab + 9b²

4) (3m²+4n²)= (3m²)² + 2 (3m²) (4n²) (4n²)²
=9m⁴+24m²n²+16n⁴6

5)(5d³+6e⁴)=(5d³)²+ 2 (5d³)(6e⁴)+(6e⁴)²
=25d⁶+60d³e⁴+36e⁸

6)(7x³+8y⁴)²= (7x³)² + 2 (7x³) (8y⁴)+ (8y⁴)²=49x⁶+106x³y⁴+64y

Otros ejercicios
1) (2/3w²-7x³)²= (2/3w²)²+ 2 (2/3w²) (-7x³) + (-7x³)
=4/9w⁴-28/3w²x³-49x⁶
2) (7x⁴+9/5y⁵)²= (7x⁴)² +2 (7x⁴) (9/5y⁵) +(9/5y⁵)²
= 49x⁸ + 153/5x⁴y⁵+81/25y¹⁰
3) (9/6a²–3/4b⁴)²= (9/6a²)²+ 2 (9/6a²) (–3/4b⁴)+(–3/4b⁴)²=81/36a⁴–54/24a²b⁴–9/16b⁸
4) (w³+14/9x⁵)²= (w³)²+ 2 (w³) (14/9x⁵) + (14/9x⁵)²
=w⁶+28/9w³x⁵+196/81x¹⁰
5) (12m – 13n³)²= (12m)²+ 2 (12m) (–13n³) +(–13n³)²
=144m²–312mn³–169n⁶
6) (9/8x³+15y⁴)²= (9/8x³)² +2 (9/8x³) (15y⁴) + (15y⁴)²
= 81/64x⁶+ 270/8 x³y⁴+225y⁸
7) (15d³+ 17e⁴)²= (15d³)²+2(15d³) (17e⁴) + (17e⁴)²=225d⁶+510d³e⁴+289e⁸
8) (8/10c⁴–19d⁵)²= (8/10c⁴)²+2(8/10c⁴) (–19d⁵) + (–19d⁵)²
=64/100c⁸–304/10c⁴d⁵–361d¹⁰
9) (4/6d²–9e³)²= (4/6d²)²+2(4/6d²) (–9e³)+ (–9e³)²
=16/36d⁴–72/6d²e³–81e⁶
10) (17f⁴+18g⁵)²= (17f⁴)²+ 2(17f⁴) (18g⁵)+ (18g⁵)²
=289f⁸+612f⁴g⁵+324g¹⁰
11) (8m²–9/6n³)²= (8m²)²+2(8m²) (–9/6n³)+ (–9/6n³)²=64m⁴–144/6m²n³–81/36n³
12) (14/7r³+16t⁴)²= (14/7r³)²+2(14/7r³) (16t⁴)+ (16t⁴)²
=196/49r⁶+448/7r³t⁴+256t⁸
13) (19m⁴–13m⁵)²= (19m⁴)²+2(19m⁴) (–13m⁵)+ (–13m⁵)²
=361m⁸–494m⁴n⁵–169m¹⁰
14) (11/7a²+14/9b³)² = (11/7a²)²+2(11/7a²) (14/9b³)+ (14/9b³)²
=121/49a⁴+308/64a²b³+96/80b⁶15) (7m⁵–9/10n⁶)²= (7m⁵)²+2(7m⁵) (–9/10n⁶)+ (–9/10n⁶)²
=49m¹⁰–126/10m⁵n⁶–81/100n⁶

DIFERENCIA DE BINOMIO
Ahora el segundo termino del TCP será negativo:

1)(x-y)²=(x) ² +2(x)(-y) + (-y) ²
x² -+2xy +y²
2)(2m-3n)²=(2m)² +2(2m)(-3n) +(-3n)²
4m²-12mn+9n²
3)(3x²-4y⁵)²=(3x²)² +2(3x²)(-4y⁵) +(-4y⁵)²9x⁴-24x²y⁵+16¹⁰
4)(²/₃b⁴-6n⁶)²=(²/₃b⁴)² +2(²/₃b⁴)(-6n⁶) +(-6n⁶)²
⁴/₉b⁸-²⁴/₃b⁴n⁶+36n¹²
5)(12w³-⁶/₈x⁴)²=(12w³)² +2(12w³)(-⁶/₈x⁴) +(-⁶/₈x⁴)²
144w⁶-¹⁴⁴/₈w³x⁴+³⁶/₆₄x⁸
6)( ⁶/₈x⁴-⁷/₆y⁵)²= (⁶/₈x⁴)² +2(⁶/₈x⁴)(-⁷/₆y⁵) +(-⁷/₆y⁵)²
³⁶/₆₄x⁸-⁸⁴/₄₈x⁴y⁵+⁴⁹/₃₆y¹⁰
EJERCICIÓS
1) (³/₄m⁴-6n⁶)²=(³/₄m⁴)² +2...