Алгебра, задания вроде как простые (8-9 класс), но не могу решить Разложить на множители: x^3+x^2y-xy^2-y^3 a^2+2ab+b^2-ac-bc m^2+2mn+n^2-p^2+2pq-q^2 x^5-x^3+x^2-1 a^3-8+6a^2-12a a^4+a^3+a+1 x^3-x^2y-xy^2+y^3
Решите задачу:
1) x³+x²y-xy²-y³=(x³-y³)+(x²y-xy²)=(x-y)(x²+xy+y²)+xy(x-y)= =(x-y)(x²+xy+y²+xy)=(x-y)(x²+2xy+y²)=(x-y)(x+y)² 2) a²+2ab+b²-ac-bc=(a²+2ab+b²)-(ac+bc)=(a+b)²-c(a+b)= =(a+b)(a+b-c) 3) m²+2mn+n²-p²+2pq-q²=(m²+2mn+n²)-(p²-2pq+q²)= =(m+n)² - (p-q)² = (m+n-p+q)(m+n+p-q) 4) x⁵-x³+x²-1=(x⁵-x³)+(x²-1)=x³(x²-1)+(x²-1)=(x²-1)(x³+1)= =(x-1)(x+1)(x+1)(x²-x+1)=(x+1)²(x-1)(x²-x+1) 5) a³-8+6a²-12a=(a³-8)+(6a²-12a)=(a³-2³)+6a(a-2)= =(a-2)(a²+2a+4)+6a(a-2)=(a-2)(a²+2a+4+6a)= =(a-2)(a²+8a+4) 6) a⁴+a³+a+1=(a⁴+a³)+(a+1)=a³(a+1)+(a+1)=(a+1)(a³+1)= =(a+1)(a³+1³)=(a+1)(a+1)(a²-a+1)=(a+1)²(a²-a+1) 7) x³-x²y-xy²+y³=(x³+y³)-(x²y+xy²)=(x+y)(x²-xy+y²)-xy(x+y)= =(x+y)(x²-xy+y²-xy)=(x+y)(x²-2xy+y²)=(x+y)(x-y)²