Question

Bài 6: Phân tích đa thức thành nhân tử

f) \(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)

Answer 1

       \(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right).\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1-3xy\right]\)

\(=\left(x+y-1\right).\left[x^2+2xy+y^2+x+y+1-3xy\right]\)

\(=\left(x+y-1\right)\left(x^2+y^2-xy+x+y+1\right)\)

Chúc bạn học tốt.

Answer 2

\(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)

\(\Leftrightarrow\left(x+y-1\right)\left(\left(x+y\right)^2+\left(x+y\right).1+1^2\right)-3xy\left(x+y-1\right)\)

\(\Leftrightarrow\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)

\(\Leftrightarrow\left(x+y-1\right)\left(x^2-xy+y^2+x+y+1\right)\)