Question

phân tích đa thức thành nhân tử:

a) 2x² - 5xy + 3y²

d) x² ( y - z ) + y² ( z - x ) + z² ( x - y )

Answer 1

d) \(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)

\(=x^2\left(y-z\right)+y^2\left[\left(z-y\right)-\left(x-y\right)\right]+z^2\left(x-y\right)\)

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

\(=\left(y-z\right)\left(x^2-y^2\right)-\left(x-y\right)\left(y^2-z^2\right)\)

\(=\left(y-z\right)\left(x-y\right)\left(x+y\right)-\left(x-y\right)\left(y-z\right)\left(y+z\right)\)

\(=\left(y-z\right)\left(x-y\right)\left(x+y-y-z\right)\)

\(=\left(y-z\right)\left(x-y\right)\left(x-z\right)\)

Answer 2

a) \(2x^2-5xy+3y^2\)

\(=2x^2-2xy-3xy+3y^2\)

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

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

Answer 3

\(a.\)\(2x^2-5xy+3y^2\)

\(=2x^2-2xy-3xy+3y^2\)

\(=\left(2x^2-2xy\right)-\left(3xy-3y^2\right)\)

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

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