Chứng minh `(x^2 - xy - y) . (x + y) + xy . (y + 1) = x^3 - y^2`

Đáp án:

$\text{Ta cs:}$

$VT= (x^2-xy-y).(x+y)+xy.(y+1)$

$= [x.(x^2-xy-y)+y.(x^2-xy-y)]+xy^2+xy$

$= x^3-x^2y-xy+x^2y-xy^2-y^2+xy^2+xy$

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

$= x^3-y^2=VP$ $(đpcm)$

$\text{Vậy }$ $(x^2-xy-y).(x+y)+xy.(y+1)=x^3-y^2$