Question

Factorizacion de la diferencia de cubos:
m³-125
1+343n³
8a³+27b³
64m³-729
27x³+64y⁶
512a⁶-27b⁹
m³n⁶-216n⁹
1000x³-y12

Answer 1

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)