Question

Tìm đa thức P biết:

a) P + ( 4x² - 5xy - y² ) = 5x² + 10xy - 2y²

b) ( 2xy + y² ) - P = 3x² -6xy + y²

Answer 1

a) \(P+\left(4x^2-5xy-y^2\right)=5x^2+10xy-2y^2\)

\(P=5x^2+10xy-2y^2-4x^2+5xy+y^2\)

\(P=x^2+15xy-y^2\)

Vậy....

b) \(\left(2xy+y^2\right)-P=3x^2-6xy+y^2\)

\(P=2xy+y^2-3x^2+6xy-y^2\)

\(P=-3x^2+8xy\)

Vậy....

Answer 2

a)    P + ( 4x² - 5xy - y² ) = 5x² + 10xy - 2y²

<=> P = 5x² + 10xy - 2y² - ( 4x² - 5xy - y² )

           = 5x² + 10xy - 2y² - 4x² + 5xy + y²

           = x² + 15xy - y²

b)    ( 2xy + y² ) - P = 3x² -6xy + y²

<=> P = ( 2xy + y²) - ( 3x² - 6xy + y² )

           = 2xy + y² - 3x² + 6xy -y²

           = 8xy - 3x²