Factorizacion de la diferencia de cubos : m³ - 125 1 + 343n³ 8a³ + 27b³ 64m³ - 729 27x³ + 64y⁶ 512a⁶ - 27b⁹ m³n⁶ - 216n⁹ 1000x³ - y12.
En resumen
1) m³ - 125 = m³ - 5³ (m - 5)(m² + (m)(5) + 5²) (m - 5)(m² + m5 + 25) 2. 1 + 343n³ = 1 + (7n)³ (1 + 7n)(1² - (1)(7n) + (7n)²) (1 + 7n)(1² - 7n + 49n²) 3. 8a³ + 27b³ = (2a)³ + 3³ (2a + 3)((2a)² - (2a)(3) + 3²) (2a + 3)(4a² - 6a + 9) 4.
1)
m³ - 125 = m³ - 5³
(m - 5)(m² + (m)(5) + 5²)
(m - 5)(m² + m5 + 25)
2.
1 + 343n³ = 1 + (7n)³
(1 + 7n)(1² - (1)(7n) + (7n)²)
(1 + 7n)(1² - 7n + 49n²)
3.
8a³ + 27b³ = (2a)³ + 3³
(2a + 3)((2a)² - (2a)(3) + 3²)
(2a + 3)(4a² - 6a + 9)
4.
64m³ - 729 = (4m)³ - 9³
(4m - 9)((4m)² + (4m)(9) + 9²)
(4m - 9)(16m² + 36m + 81)
5.
27x³ + 64y ^ 6 = (3x)³ + (4y²)³
(3x + 4y²)((3x)² - (3x)(4y²) + 4²)
(3x + 4y²)(9x² - 12xy² + 16)
6.
512a ^ 6 - 27b ^ 9 = (8a²)³ - (3b³)³
(8a² - 3b³)((8a²)² + (8a²)(3b³) + (3b³)²
(8a² - 3b³)(64a⁴ + 24a²b³ + 9b ^ 6)
7.
M³n ^ 6 - 216n ^ 9 = (mn²)³ - 6³
(mn² - 6)((mn²)² + (mn²)(6) + 6²)
(mn² - 6)(m²n⁴ + mn²6 + 36
8.
1000x³ - y ^ 12 = (10x)³ - (y⁴)³
(10x + y⁴)((10x)² - (10x)(y⁴) + (y⁴)²
(10x + 4y⁴)(100x² - 10xy⁴ + y ^ 8).
Factorizar. Caso : Factor Común. (x² + 2)(m - n) + 2(m - n) = Sacas factor común (m - n) (m - n)(x² + 2 + 2) = (m - n)(x² + 4) Respuesta. (m - n)(x² + 4).
M ala n = 81 Mn = 12 M = 3 N = 4.
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