Question

Разложить на множители:
1)18a²-2
2) 2ax³-16ay³
3) 8k⁴+8k²+2
4) 9m²-6m-10p-25p²
5) a³+3a²x+6ax+12x-8

Answer 1

1)18a²-2=2(9a²-1)=2(3a-1)(3a+1)
2) 2ax³-16ay³=2a(x³-8y³)=2a(x-2y)(x²+2xy+4y²)
3) 8k⁴+8k²+2=2(4k⁴+4k²+1)=2(2k²+1)
4) 9m²-6m-10p-25p²=(9m²-25p²)-(6m+10p)=(3m-5p)(3m+5p)-2(3m+5p)=
   =(3m+5p)(3m-5p-2)
5) a³+3a²x+6ax+12x-8=(a³-8)+3x(a²+2a+4)=(a-2)(a²+2a+4)+3x(a²+2a+4)=
   =(a²+2a+4)(a-2+3x)