Разложение ** множители 1)m^3-n^3-6m(m^2+mn+n^2); 2)p^3+q^3-2pq(p^2-pq+q^2)

Question

Разложение на множители 1)m^3-n^3-6m(m^2+mn+n^2);
2)p^3+q^3-2pq(p^2-pq+q^2)

Answer 1

M³-n³-6m(m²+mn+n²)=(m-n)(m²+mn+n²)-6m(m²+mn+n²)=
=(m²+mn+m²)(m-n-6m)=(m²+mn+n²)(-n-5m)=-(m²+mn+n²)(n+5m)
p³+q³-2pq(p²-pq+q²)=(p+q)(p²-pq+q²)-2pq(p²-pq+q²)=(p²-pq+q²)(p+q-2pq)

Answer 2

1)(m-n)(m^2+mn+n^2)-6m (m^2+mn+n^2)=(m^2+mn+n^2)(-5m-n)=-(5m+n)(m^1+mn+n^2)
2)(p+q)(p^2-pq+q^2)-2pq (p^2-pq+q^2)=(p-2pq+q)(p^2-pq+q^2)