Question

Разложите на множители

[] там будет указывать степень

1)x[3] +y[3] +2xy(x+y)

2)8b[3] +6b[2] +3b+1

3)a[3] - 2a[2] +2a-1

Answer 1

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

8b³+6b³+3b+1=(2b+1)(4b²-2b+1)+3b(2b+1)=(2b+1)(4b²-2b+1+3b)=
=(2b+1)(4b²+b+1)

a³-2a²+2a-1=(a-1)(a²+a+1)-2a(a-1)=(a-1)(a²+a+1-2a)=(a-1)(a²-a+1)