[Toán 8] Phân tích đa thức thành nhân tử.

I

icy_tears

$3xyz + x(y^2 + z^2) + y(x^2 + z^2) + z(x^2 + y^2)$ (Chắc đề thế này)

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

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

$= xy(x + y + z) + z^2(x + y) + z(x + y)^2$

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

$= (xy + yz + zx)(x + y + z)$
 
H

harrypham

$$\begin{aligned} 3xyz+x(y^2+z^2)+y(x^2+z^2)+z(x^2+y^2) & = 3xyz+xy^2+xz^2+yx^2+yz^2+zx^2+zy^2 \\ & = (xy^2+yx^2)+(zx^2+xyz)+(zy^2+xyz)+(z^2x+xyz+z^2y) \\ & = xy(x+y)+xz(x+y)+yz(x+y)+z(xz+xy+yz) \\ & = (xy+xz+yz)(x+y)+(xy+xz+yz)z \\ & = (x+y+z)(xy+xz+yz) \end{aligned}$$
 
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