Lawson Bates
04/12/2023 · High School
f) \( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} \) g) \( m^{2}-n^{2} \)
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Claro, aquí tienes las soluciones para los problemas de estudio:
f) \( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} \)
Este polinomio es una expansión de la diferencia de cubos, que se puede escribir como:
\[ a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2}) \]
Aplicando esta fórmula a tu expresión, obtenemos:
\[ a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} = (a - b)(a^{2} + ab + b^{2}) \]
g) \( m^{2}-n^{2} \)
Este es un caso de la fórmula de la diferencia de cuadrados, que se puede escribir como:
\[ m^{2} - n^{2} = (m + n)(m - n) \]
Aplicando esta fórmula a tu expresión, obtenemos:
\[ m^{2} - n^{2} = (m + n)(m - n) \]
Espero que estas soluciones te sean útiles para tu estudio.
Quick Answer
f) \( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} = (a - b)(a^{2} + ab + b^{2}) \)
g) \( m^{2}-n^{2} = (m + n)(m - n) \)
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