MatemáticasBásico1 respuestas

Simplificar : C = (a - b)[(a + b) ^ 2 + (a - b) ^ 2 + 2ab] + 2b ^ 3?

Simplificar : C = (a - b)[(a + b) ^ 2 + (a - b) ^ 2 + 2ab] + 2b ^ 3.

9Natismamu4871

En resumen

La expresión simplificada C = (a - b)[(a + b) ^ 2 + (a - b) ^ 2 + 2ab] + 2b ^ 3 queda : <img src="https://tex.z-dn.net/?f=C%20%3D%202a%5E3" />Simplificación por pasos<img src="https://tex.z-dn.net/?

Mejor respuesta

Chonito123

1

La expresión simplificada C = (a - b)[(a + b) ^ 2 + (a - b) ^ 2 + 2ab] + 2b ^ 3 queda : <img src="https://tex.z-dn.net/?f=C%20%3D%202a%5E3" />Simplificación por pasos<img src="https://tex.z-dn.net/?f=%5Cleft%28a-b%5Cright%29%5Cleft%28%5Cleft%28a%2Bb%5Cright%29%5E2%2B%5Cleft%28a-b%5Cright%29%5E2%2B2ab%5Cright%29%2B2b%5E3" />Expandiendo : <img src="https://tex.z-dn.net/?f=%5Cleft%28a%2Bb%5Cright%29%5E2%3A%5Cquad%20a%5E2%2B2ab%2Bb%5E2%5Cleft%28a-b%5Cright%29%5E2%3A%5Cquad%20a%5E2-2ab%2Bb%5E2" /><img src="https://tex.z-dn.net/?f=%5Cleft%28a%2Bb%5Cright%29%5E2%2B%5Cleft%28a-b%5Cright%29%5E2%2B2ab%20%3Da%5E2%2B2ab%2Bb%5E2%2Ba%5E2-2ab%2Bb%5E2%2B2ab" />Simplificando : C <img src="https://tex.z-dn.net/?f=%3D%5Cleft%28a-b%5Cright%29%5Cleft%282a%5E2%2B2ab%2B2b%5E2%5Cright%29%2B2b%5E3" />Expandiendo : <img src="https://tex.z-dn.net/?f=%5Cleft%28a-b%5Cright%29%5Cleft%282a%5E2%2B2ab%2B2b%5E2%5Cright%29" /><img src="https://tex.z-dn.net/?f=%3D2a%5E2a%2B2aab%2B2ab%5E2-2a%5E2b-2abb-2b%5E2b" />Simplificando : <img src="https://tex.z-dn.net/?f=%3D2a%5E3-2b%5E3" />C<img src="https://tex.z-dn.net/?f=%3D2a%5E3-2b%5E3%2B2b%5E3" />Sumando términos similaresC<img src="https://tex.z-dn.net/?f=%3D2a%5E3" />.