Question

Разложить на множители:
x^3+y^3+2xy(x+y)
x^3-y^3-5x(x^2+xy+y^2)
x^3+y^3+2x^2-2xy+2y^2
a^3-b^3+3a^2+3ab+3b^2​

Answer 1

x³+y³+2xy(x+y)=(x+y)(x²-xy+y²)+2xy(x+y)=(x+y)(x²-xy+2xy+y²)=(x+y)(x²+xy+y²)

x³-y³-5x(x²+xy+y²)=(x-y)(x²+xy+y²)-5x(x²+xy+y²)=(x-y-5x)(x²+xy+y²)=(-4x-y)(x²+xy+y²)=-(4x+y)(x²+xy+y²)

x³+y³+2x²-2xy+2y²=(x+y)(x²-xy+y²)+2(x²-xy+y²)=(x+y+2)(x²-xy+y²)

a³-b³+3a²+3ab+3b²=(a-b)(a²+ab+b²)+3(a²+ab+b²)=(a-b+3)(a²+ab+b²)