Question

Chứng minh 2x + y + y2 = (1 - xy + y).(2x + y) + xy(2x + y - 2)

Answer 1

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

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

\(=2x+y+y^2\)

Answer 2

Ta có \(VP = ( 1 - xy + y) .(2x +y) + xy (2x + y -2)\)

 =  \(2x + y - 2x^{2}y - xy^{2} + 2xy + y^{2} + 2x^{2}y + xy^{2} - 2xy\)

= \(2x + y ^{2} + y = VT\)