Question

phân tích đa thức thành nhân tử \(x^2-2xy+y^2+4x-4y-5\)

Answer 1

\(x^2-2xy+y^2+4x-4y-5\)

\(=\left(x-y\right)^2+4\left(x-y\right)+4-9\)

\(=\left(x-y+2\right)^2-9\)

\(=\left(x-y+2-3\right)\left(x-y+2+3\right)\)

\(=\left(x-y-1\right)\left(x-y+5\right)\)

Answer 2

\(x^2-2xy+y^2+4x-4y-5\)

\(=\left(x-y\right)^2+4\left(x-y\right)+4-9\)

\(=\left(x-y+2\right)^2-9\)

\(=\left(x-y+2-3\right)\cdot\left(x-y+2+3\right)\)

\(=\left(x-y-1\right)\cdot\left(x-y+5\right)\)

Answer 3

\(x^2-2xy+y^2+4x-4y-5\\ =\left(x^2+y^2+4-2xy+4x-4y\right)-9\\ =\left(x-y+2\right)^2-9\\ =\left(x-y+5\right)\left(x-y-1\right)\)