Question

разложите на множители

1) (a-2b)^3+8b^3
2) 27-(x-2)^3
3) (m+1)^3+64

Answer 1

1)

Первый способ

формула

(m-n)³=m³-3m²n+3mn²-n³

m=a

n=2b

(a-2b)³+8b³=a³-3a²·2b+3a·(2b)²-8b³+8b³=a³-6a²b+12ab²=a(a²-6ab+12b²)

Второй способ

формула

m³+n³=(m+n)(m²-mn+n²)

m=a-2b

n=2b

(a-2b)³+8b³= (a-2b)³+(2b)³=(a-2b+2b)((a-2b)²-2b(a-2b)+(2b)²)=

=a(a²-4ab+4b²-2ab+4b²+4b²)=a(a²-6ab+12b²)

2) 27-(x-2)³ =3³-(x-2)³=(3-x+2)(3²+3(x-2)+(x-2)²)=(5-x)(9+3x-6+x²-4x+4)=

=(5-x)(x²-x+7)

3) (m+1)³+64=(m+1)³+4³=(m+1+4)((m+1)²-4(m+1)+16)=(m+5)(m²+2m+1-4m-4+16)=

=(m+5)(m²-2m+13)