Đáp án:
$g) (x-y+z)(x+y-z)\\
h)
(x-y)(x-y-z)\\
i) (x-2y)(x+t)\\
k) (2y+z)(x+3)\\
l) (x+2z)(x+2y)\\
m) 3(x+y)(y+z)(x+z)$
Giải thích các bước giải:
$g) x^2-y^2+2yz-z^2=x^2-(y^2-2yz+z^2)=x^2-(y-z)^2\\
=(x-y+z)(x+y-z)\\
h)
x^2-2xy+y^2-xz+yz\\
=(x-y)^2-z(x-y)=(x-y)(x-y-z)\\
i) x^2-2xy+tx-2ty\\
=x(x-2y)+t(x-2y)=(x-2y)(x+t)\\
k) 2xy+3z+6y+xz\\
=(2xy+xz)+(3z+6y)\\
=x(2y+z)+3(z+2y)\\
=(2y+z)(x+3)\\
l) x^2+2xz+2xy+4yz\\
=x(x+2z)+2y(x+2z)\\
=(x+2z)(x+2y)\\
m) (x+y+z)^3-x^3-y^3-z^3\\
=(x+y)^3+3(x+y)^2z+3(x+y)z^2+z^3-x^3-y^3-z^3\\
=x^3+3x^2y+3xy^2+y^3+3.(x^2+2xy+y^2)z+3xz^2+3yz^2+z^3-x^3-y^3-z^3\\
=x^3+3x^2y+3xy^2+y^3+3x^2z+6xyz+3y^2z+3xz^2+3yz^2+z^3-x^3-y^3-z^3\\
=(x^3-x^3)+(y^3-y^3)+(z^3-z^3)+(3x^2y+3x^2z)+(3xy^2+3xyz)+(3y^2z+3xyz)+(3xz^2+3yz^2)\\
=3x^2(y+z)+3xy(y+z)+3yz(y+x)+3z^2(x+y)\\
=3x(y+z)(x+y)+3z(x+y)(y+z)\\
=3(x+y)(y+z)(x+z)$
