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\(3,=\left(x-y\right)^3+\left(y-x+x-z\right)^3+\left(z-x\right)^3\\ =\left(x-y\right)^3+\left(y-x\right)^3+3\left(y-x\right)\left(x-z\right)\left(y-x+x-z\right)+\left(x-z\right)^3+\left(z-x\right)^3\\ =\left(x-y\right)^3-\left(x-y\right)^3+3\left(y-x\right)\left(x-z\right)\left(y-z\right)-\left(z-x\right)^3+\left(z-x\right)^3\\ =3\left(y-x\right)\left(x-z\right)\left(y-z\right)\)
\(4,=\left(x^4+3x^3-x^2\right)+\left(3x^3+9x^2-3x\right)-\left(x^2+3x-1\right)\\ =x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\\ =\left(x^2+3x-1\right)\left(x^2+3x-1\right)\\ =\left(x^2+3x-1\right)^2\)
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Do câu d mình ko biết làm bởi v mình không làm được
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a: =(x-z)(y+8)
b; =x^2-2x-3x+6
=(x-2)(x-3)
c: =x^4+10x^2-x^2-10
=(x^2+10)(x^2-1)
=(x^2+10)(x-1)(x+1)
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bn gõ bài trong công thức trực quan ik, khó nhìn lắm, ko làm đc
1). x2y2(y-x)+y2z2(z-y)-z2x2(z-x)
2)xyz-(xy+yz+xz)+(x+y+z)-1
3)yz(y+z)+xz(z-x)-xy(x+y)
5)y(x-2z)2+8xyz+x(y-2z)2-2z(x+y)2
6)8x3(y+z)-y3(z+2x)-z3(2x-y)
7) (x2+y2)3+(z2-x2)3-(y2+z2)3
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`a, 4a^2 + 4a + 1 = (2a+1)^2`
`b, -3x^2 + 6xy - 3y^2`
` = -3(x-y)^2`
`c, (x+y)^2 - 2(x+y)z + z^2`
`= (x+y-z)^2`
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\(a,=x\left(x^2-4x+4-z^2\right)=x\left[\left(x-2\right)^2-z^2\right]=x\left(x-z-2\right)\left(x+z-2\right)\\ b,=\left(x-y\right)^2-\left(z-5\right)^2=\left(x-y-z+5\right)\left(x-y+z-5\right)\)
\(x^3-4x^2+4x-xz^2=x\left(x^2-4x+4-z^2\right)\)
\(=x\left[\left(x-2\right)^2-z^2\right]=x\left(x-2-z\right)\left(x-2+z\right)\)
\(x^2-2xy+y^2-z^2+10z-25\)
\(=\left(x-y\right)^2-\left(z-5\right)^2\)
\(=\left(x-y+z-5\right)\left(x-y-z+5\right)\)
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`a, P = 2x(3 - x^2)`
`b, Q = 5x^2(x-3y)`
`c, R = xy(3x^2y^2 - 6y^2z + 1)`
a) \(P=6x-2x^3\)
\(P=2x\left(3+x^2\right)\)
b) \(Q=5x^3-15x^2y\)
\(Q=5x^2\left(x-3y\right)\)
c) \(R=3x^3y^3-6xy^3z+xy\)
\(R=xy\left(3x^2y^2-6y^2z+1\right)\)
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\(a,=6x\left(x-2\right)-7\left(x-2\right)=\left(6x-7\right)\left(x-2\right)\)
\(A=x^2y^3-x^3y^2+y^2z^3-y^3z^2-z^3x^2+x^3z^2\)
\(A=\left(x^2y^3-x^2z^3\right)+\left(x^3z^2-x^3y^2\right)+\left(y^2z^3-y^3z^2\right)\)
\(A=x^2\left(y^3-z^3\right)-x^3\left(y^2-z^2\right)-y^2z^2\left(y-z\right)\)
\(A=\left(y-z\right)\left(x^2y^2+x^2yz+x^2z^2-x^3y-x^3z-y^2z^2\right)\)
\(A=\left(y-z\right)\left[\left(x^2y^2-x^3y\right)+\left(x^2yz-x^3z\right)+\left(x^2z^2-y^2z^2\right)\right]\)
\(A=\left(y-z\right)\left[x^2y\left(y-x\right)+x^2z\left(y-x\right)-z^2\left(y^2-x^2\right)\right]\)
\(A=\left(y-z\right)\left(y-x\right)\left(x^2y+x^2z-z^2y-z^2x\right)\)
\(A=\left(y-z\right)\left(y-x\right)\left[y\left(x^2-z^2\right)+xz\left(x-z\right)\right]\)
\(A=\left(y-z\right)\left(y-x\right)\left(x-z\right)\left(xy+yz+zx\right)\)
\(A=\left(x-y\right)\left(y-z\right)\left(z-x\right)\left(xy+yz+zx\right)\)