Question

1: разложите на множители: 1)x^3+64; 2)125-x^3; 3)27a^3-64b^3; 4)1+27m^3 2: разложите на множители: 1)a^3+b^3-2ab(a+b); 2)m^3-n^3-6m(m^2+mn+n^2); 3)x^3-y^3+8x^2y-8xy^2; 4)p^3+q^3-2pq(p^2-pq+q^2) условные обозначения: ^-степень

Answer 1

1.

1)x³+64=х³+4³=(х+4)(х²-4х+16);
2)125-x³=5³-х³=(5-х)(25+5х+х²);
3)27a³-64b³=(3a)³-(4b)³=(3a-4b)(9a²-12ab+16b²);
4)1+27m³=1+(3m)³=(1+3m)(1-3m+9m²)
2.
1)a³+b³-2ab(a+b)=(a+b)·(a²-ab+b²)-2ab·(a+b)=(a+b)(a²-ab+b²-2ab)=
=(a+b)(a²-3ab+b²);
2)m³-n³-6m(m²+mn+n²)=(m-n)(m²+mn+n²)-6m(m²+mn+n²)=
=(m²+mn+n²)·(m-n-6m)=(m²+mn+n²)·(-n-5m)=-(m²+mn+n²)·(n+5m);
3)x³-y³+8x²y-8xy²=(x-y)(x²+xy+y²)-8xy(x-y)=(x-y)·(x²+xy+y²-8xy)=
=(x-y)·(x²-7xy+y²);
4)p³+q³-2pq(p²-pq+q²)=(p+q)(p²-pq+q²)-2pq·(p²-pq+q²)=(p²-pq+q²)·(p+q-2pq)