Apuntes Del 2 De Septiembre Del 2008

Binomio Al Cuadrado
1.
(2a + b) ^ 2 = ( PT) ^ 2 + 2 (PT)(ST) + (ST) ^ 2

= ( 2a) ^ 2 + 2 (2a)(b) + (b) ^ 2

= 4a + 4ab + b^2


2.
(3x + 4y) ^ 2 = ( 3x) ^ 2 + 2 (3x)(4y) + (4y) ^ 2

= 9x ^2 + 24xy + 16y


3.
(3a^2 + 6b^3) ^ 2 = ( 3a^2) ^ 2 + 2 (3a^2)(6b^3) + (6b^3) ^ 2

= 9a ^4 + 36a^2b^3+ 36b^6

4.
(4x^3 - 2y^2) ^ 2 = ( 4x^3) ^ 2 + 2 (4x^3)(2y^2) + (2y^2) ^ 2

= 16x^6 - 16x^3y^2+ 4y^4


Binomio Al Cubo

1.
(2x^2 + 3y^3)^3 = ( PT) ^ 3 + 3 (PT)^2 (ST) + 3 (PT) (ST)^2 + (ST) ^ 3

= ( 2x^2) ^ 3 + 3 (2x^2)^2 (3y^3) + 3 (2x^2) (3y^3)^2 + (3y^3) ^ 3

= 8x^6 + (6x^4) (3y^3) + (6x^2) (9y^6) + 27y^9

= 8x^6 + 36x^4+ 54x^2 y^6 + 27 y^9

2.
(3a^3 - 3b^2)^3 = ( PT) ^ 3 + 3 (PT)^2 (ST) + 3 (PT) (ST)^2 + (ST) ^ 3

= ( 3a^3) ^ 3 + 3 (3a^3)^2 (3b^2) + 3 (3a^3) (3b^2)^2 + (3b^2) ^ 3

= 27a^9 - 81a^6 b^2 + 9a^3 9b^4 + 27b^6