Question

phân tích thành nhân tử
\(x^3+3xy+y^3-1\)
 

Answer 1

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

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

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

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

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

Answer 2

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

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

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

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

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