\(xyz-\left(xy+yz+xz\right)+\left(x+y+z\right)-1\)

\(=xyz-xy-yz+y-xz+x+z-1\)

\(=xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+z-1\)

\(=\left(xy-y-x+1\right)\left(z-1\right)\)

\(=[\left(x-1\right)y-\left(x-1\right)]\left(z-1\right)\)

\(=\left(x-1\right)\left(y-1\right)\left(z-1\right)\)

b) Ta có: \(x^3-x^2y-xy^2+y^3\)

\(=\left(x^3+y^3\right)-\left(x^2y+xy^2\right)\)

\(=\left(x+y\right)\left(x^2-xy+y^2\right)-xy\left(x+y\right)\)

\(=\left(x+y\right)\left(x^2-2xy+y^2\right)\)

\(=\left(x+y\right)\left(x-y\right)^2\)

       \(xyz-\left(xy+yz+xz\right)+\left(x+y+z\right)-1\)

\(=\left(xyz-xy-xz+x\right)-yz+y+z-1\)

\(=x\left(yz-y-z+1\right)-\left(yz-y-z+1\right)\)

\(=\left(x-1\right)\left(yz-y-z+1\right)\)

\(=\left(x-1\right)\left[y\left(z-1\right)-\left(z-1\right)\right]\)

\(=\left(x-1\right)\left(y-1\right)\left(z-1\right)\)

xy(x+y)+yz(y+z)+xz(x+z)+2xyz 

= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 

= xy(x + y) + yz(y + z + x) + xz(x + z + y) 

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

= (x + y)(y + z)(z + x)

 xy(x+y)+yz(y+z)+xz(x+z)+2xyz 

= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 

= xy(x + y) + yz(y + z + x) + xz(x + z + y) 

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

= (x + y)(y + z)(z + x)

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.

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 xy(x+y)+yz(y+z)+xz(x+z)+2xyz 

= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 

= xy(x + y) + yz(y + z + x) + xz(x + z + y) 

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

= (x + y)(y + z)(z + x)

\(xy\left(x-y\right)+yz\left(y-z\right)+xz\left(z-x\right)\)

\(=xy\left(x-y\right)+yz\left[\left(y-x\right)-\left(z-x\right)\right]+xz\left(z-x\right)\)

\(=xy\left(x-y\right)-yz\left(x-y\right)-yz\left(z-x\right)+xz\left(z-x\right)\)

\(=\left(x-y\right)\left(xy-yz\right)-\left(z-x\right)\left(yz-xz\right)\)

\(=\left(x-y\right)\left(xy-yz\right)+\left(z-x\right)\left(xz-yz\right)\)

\(=\left(xy-yz\right)\left(x-y+z-x\right)\)

\(=\left(xy-yz\right)\left(-y+z\right)\)

mơn bn nha ^^

nh sáng nay lên lp thầy chữa bài thì kq nó k như z, cả cách lm nx :v

kq là: ( z - y )( x - z)( y - x )

[ вơ đắйǥ ] вé เςë ⁀ᶜᵘᵗᵉ

Ukm cảm ơn nhé quên mất đoạn cuối vẫn phân tích đc nữa

\(a,=\left(xy-1-x-y\right)\left(xy-1+x+y\right)\\ b,Sửa:a^3+2a^2+2a+1\\ =a^3+a^2+a^2+a+a+1=\left(a+1\right)\left(a^2+a+1\right)\\ c,=1-4a^2-a\left(a^2-4\right)=1-4a^2-a^3+4a\\ =\left(1-a\right)\left(1+a+a^2\right)+4a\left(1-a\right)\\ =\left(1-a\right)\left(1+5a+a^2\right)\\ d,=\left(a^2-a^2b^2\right)+\left(b^2-b\right)+\left(ab-a\right)\\ =a^2\left(1-b\right)\left(1+b\right)+b\left(b-1\right)+a\left(b-1\right)\\ =\left(b-1\right)\left(-a^2-ab+b+a\right)\\ =\left(b-1\right)\left(b-1\right)\left(a+b\right)\left(1-a\right)\)

\(e,=x^2y+xy^2-yz\left(y+z\right)+x^2z-xz^2\\ =\left(x^2y+x^2z\right)+\left(xy^2-xz^2\right)-yz\left(y+z\right)\\ =x^2\left(y+z\right)+x\left(y-z\right)\left(y+z\right)-yz\left(y+z\right)\\ =\left(y+z\right)\left(x^2+xy-xz-yz\right)\\ =\left(y+z\right)\left(x+y\right)\left(x-z\right)\)

\(f,=xyz-xy-yz-xz+x+y+z-1\\ =xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+\left(x-1\right)\\ =\left(z-1\right)\left(xy-y-x+1\right)=\left(z-1\right)\left(x-1\right)\left(y-1\right)\)