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Cubos de Binomio

Cubos de Binomio. Descomposición visual de cubo de binomio. Cubo de Binomio. (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3. El cubo de la arista a + b, se puede separar en 8 cuerpos como lo ilustra la figura, entonces:. V 1 = a 3 V 4 = a 2 b V 7 = b 3. V 2 = a 2 b V 5 = a 2 b V 8 = ab 2.

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Cubos de Binomio

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  1. Cubos de Binomio

  2. Descomposición visual de cubo de binomio.

  3. Cubo de Binomio (a + b)3 = a3 + 3a2b + 3ab2 + b3 El cubo de la arista a + b, se puede separar en 8 cuerpos como lo ilustra la figura, entonces: V1= a3 V4= a2b V7= b3 V2= a2b V5= a2b V8= ab2 V3= ab2 V6= ab2 Si sumamos los 8 Volúmenes, obtenemos: (a + b)3 = a3 + 3a2b + 3ab2 + b3 Si en la fórmula anterior sustituyes b por –b, se obtiene: (a - b)3 = a3 - 3a2b + 3ab2 - b3

  4. Fórmula (a + b)3 = a3 + 3a2b + 3ab2 + b3 Ejemplos: (2a+3b)3 = (2a)3 + 3(2a)2 · 3b +3 · (2a) · (3b)2+(3b)3 8a3+36a2b+54ab2+27b3

  5. Ejemplos (2a+3b)3 = Fórmula a aplicar: (a + b)3 = a3 + 3a2b + 3ab2 + b3 Reemplazamos “a” por “2a” y “b” por “3b” (2a)3 + 3(2a)2 · 3b + 3 · (2a) · (3b)2 + (3b)3 Resultado: 8a3 + 36a2b + 54ab2 + 27b3

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