Разложите ** множители m^3n^3-6m(m^2+mn+n^2) 2. x^3-y^3+8x^2y-8xy^2 3. p^3+g^3-2pg...

Question

Разложите на множители
m^3n^3-6m(m^2+mn+n^2)
2. x^3-y^3+8x^2y-8xy^2 3. p^3+g^3-2pg (p^2-pg+p^2)
очень надо быстро помогите

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Answer 1

A³-b³=(a-b)(a²+ab+b²)  a³+b³=(a+b)(a²-ab+b²)
1) m³-n³-6m(m²+mn+n²)=(m-n)(m²+mn+n²)-6m(m²+mn+n²)=(m-n-6m)(m²+mn+n²)=-(5m+n)(m²+mn+n²)
2) x³-y³+8x²y-8xy²=(x-y)(x²+xy+y²)+8xy(x-y)=(x-y)(x²+xy+y²+8xy)=(x-y)(x²+9xy+y²)
3) p³+q³-2pq(p²-pq+q²)=(p+q)(p²-pq+q²)-2pq(p²-pq+q²)=(p+q-2pq)(p²-pq+q²)