Respuestas
Respuesta:
Artificio de criterios exponenciales
Artificio de diferencia de cubos
espero haberte ayudado, suerte.
Respuesta:
Explicación paso a paso:
Todo es suma y diferencia de cubos
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
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∴
a.
216m⁶ - 1331
= (6m²)³ - 11³
= [6m² - 11] [(6m²)² + (6m²)(11) + 11²]
= [6m² - 11] [36m⁴ + 66m² + 121]
b.
512a⁶ - 8b³
= (8a²)³ - (2b)³
= [8a² - 2b] [(8a²)² + (8a²)(2b) + (2b)²]
= [8a² - 2b] [64a⁴ + 16a²b + 4b²] sacamos cuarta
= [8a² - 2b] 4[16a² + 4a²b + b²] mitad
= 2[4a² - b] 4[16a² + 4a²b + b²]
= 8[4a² - b] [16a² + 4a²b + b²]
c.
m³/8 - 1/27
= (m/2)³ - (1/3)³
= [m/2 - 1/3] [(m/2)² + (m/2)(1/3) + (1/3)²]
= [m/2 - 1/3] [m²/4 + m/6 + 1/9]
d.
1 + 1000m³
= 1³ + (10m)³
= [1 + 10m} [ 1² - (1)(10m) + (10m)² ]
= [1 + 10m] [ 1 - 10m + 100m²]