Question

Cho đa thức P= 5x^2y - 2xy^2 + xy - x + y - 2

a) Tìm đa thức R,biết rằng P + R = -xy × (x - y)

Answer 1

\(P+R=-xy\cdot(x-y)\\\Leftrightarrow R=-xy(x-y)-P\\\Leftrightarrow R=-x^2y+xy^2-(5x^2y-2xy^2+xy-x+y-2)\\\Leftrightarrow R=-x^2y+xy^2-5x^2y+2xy^2-xy+x-y+2\\\Leftrightarrow R=(-x^2y-5x^2y)+(xy^2+2xy^2)-xy+x-y+2\\\Leftrightarrow R=-6x^2y+3xy^2-xy+x-y+2\)

Answer 2

Ta có:

\(P+R=-xy\cdot\left(x-y\right)\)

\(\Leftrightarrow\left(5x^2y-2xy^2+xy-x+y-2\right)+R=-x^2y+xy^2\)

\(\Leftrightarrow R=-x^2y+xy^2-5x^2y+2xy^2+xy+x-y+2\)

\(\Leftrightarrow R=\left(-x^2y-5x^2y\right)+\left(xy^2+2xy^2\right)+xy+x-y+2\)

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