toán lớp 8 : phân tích đa thức thành nhân tử

P

pinkylun

a) $x^3+y^3+z^3-3xyz$

$=(x+y)^3-3xy(x+y)+z^3-3xyz$

$=(x+y+z)^3-3z(x+y)(x+y+z)-3xy(x+y)-3xyz$

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

$=3(x+y+z)[x^2+y^2+z^2-xy-yz-xz]$

b) $(x+y+z)^3 - x^3 -y^3 - z^3$

$=(x+y)^3+z^3+3z(x+y)(x+y+z)-x^3-y^3-z^3$

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

$=3(x+y)(xy+xz+yz+z^2)$

$=3(x+y)(y+z)(x+z)$

c) $x^2-2xy+y^2-xy+yz=(x-y)^2-y(x-z)=???$

d) $x^2-25+y^2+2xy=(x+y)^2-25=(x+y-5)(x+y+5)$

e) $ (x+y)^2-(x^2-y^2)=(x+y)^2-(x+y)(x-y)=(x+y)(x+y-x+y)=2y(x+y)$


 
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