1) Ta có : $(x^2+2x+1) = (x+1)^2$
$⇒(x^2+2x+1) : (x+1) = (x+1)^2 : (x+1) = x+1$
2) $(x+y)^2-(x-y)^2 = x^2+2xy+y^2-x^2+2xy-y^2=4xy$
3)
a) $x^2+3x+3y+xy$
$=x(x+y)+3(x+y)$
$=(x+y)(x+3)$
b) $x^3+5x^2+6x$
$=x.(x^2+5x+6)$
$=x.(x^2+2x+3x+6)$
$=x(x+2)(x+3) $
4) Ta có :
$(x+y+z)^2 - x^2-y^2-z^2$
$=[(x+y)+z]^2 -x^2-y^2-z^2$
$=(x+y)^2 + 2(x+y).z + z^2 -x^2-y^2-z^2$
$=2.(xy+yz+zx)$
Chúc bạn học tốt !