Phân tích đa thức thành nhân tử? (toán lớp 8)

T

thong7enghiaha

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

l4s.smiledonghae

Gợi ý: Áp dụng hằng đẳng thức;
\[{x^3} + {y^3} + {z^3} = (x + y + z)({x^2} + {y^2} + {z^2} - xy - yz - xz) + 3xyz\]
 
N

noinhobinhyen

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

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

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

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

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

$=3(x+y)(y+z)(z+x)$
 
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