X-2xy+4y=-3
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a) \(3x^2-3xy-5x+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
b) \(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
c) \(x^2+1+2x-y^2\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1+y\right)\left(x+1-y\right)\)
d) \(x^2+4x-2xy-4y+y^2\)
\(=\left(x^2-2xy+y^2\right)+\left(4x-4y\right)\)
\(=\left(x-y\right)^2+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+4\right)\)
e) \(x^3-2x^2+x\)
\(=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
f) \(2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x^2+2x+1\right)+y^2\right]\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x-y+1\right)\left(x+y+1\right)\)
a: =3x(x-y)-5(x-y)
=(x-y)(3x-5)
b: \(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
d:
Sửa đề: x^2+4x-2xy-4y+y^2
=x^2-2xy+y^2+4x-4y
=(x-y)^2+4(x-y)
=(x-y)(x-y+4)
e: =x(x^2-2x+1)
=x(x-1)^2
f: =2(x^2+2x+1-y^2)
=2[(x+1)^2-y^2]
=2(x+1+y)(x+1-y)
![](https://rs.olm.vn/images/avt/0.png?1311)
(x3 - 4y)(x2 - 2xy + 4y)(x2 + 2xy + 4y) tại x = -2; y = 1/2
Thay x = -2; y = 1/2 vào biểu thức, ta có:
[(-2)3 - 4.(1/2)].[(-2)2 - 2.(-2).(1/2) + 4.(1/2)].[(-2)2 + 2.(-2).(1/2) + 4.(1/2)]
= -10.8.4
= -320
Vậy:..
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(x^2-4y^2\right)\left(x^2-2xy+4y^2\right)\left(x^2+2xy+4y^2\right)\)
\(A=\left(x-2y\right)\left(x+2y\right)\left(x^2-2xy+4y^2\right)\left(x^2+2xy+4y^2\right)\)
\(A=\left(x-2y\right)\left(x^2+2xy+4y^2\right)\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
\(A=\left[x^3-\left(2y\right)^3\right]\left[x^3+\left(2y\right)^3\right]\)
\(A=\left[x^3-8y^3\right]\left[x^3+8y^3\right]\)
\(A=x^6-64y^6\)
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a: \(=-xy\cdot x^2-2xy\cdot xy+3\cdot xy\)
\(=-x^3y-2x^2y^2+3xy\)
b: \(=\left(5x-x+4y-4y\right)\left(y-5x\right)\)
\(=4x\left(y-5x\right)=-20x^2+4xy\)
c: \(=\left(4x^2-2y\right)\left(5x^3-4y^2\right)\)
\(=4x^2\cdot5x^3-4x^2\cdot4y^2-2y\cdot5x^3+2y\cdot4y^2\)
\(=20x^5-16x^2y^2-10x^3y+8y^3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(x^4y-5x^4y-5xy^3+2xy^3=-4x^4y-3xy^3\)
b: \(5xy^4-5xy+7xy-2xy^4=3xy^4+2xy\)
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\(a,=x\left(x^3+3x^2-6x-8\right)\\ =x\left(x^3+4x^2-x^2-4x-2x-8\right)\\ =x\left(x+4\right)\left(x^2-x-2\right)\\ =x\left(x+4\right)\left(x-2\right)\left(x+1\right)\)
\(b,=x^4+36x^2+324-36x^2\\ =\left(x^2+18\right)^2-36x^2\\ =\left(x^2+6x+18\right)\left(x^2-6x+18\right)\)
\(c,=xy\left(x^3y^3+xy+2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(2x-y\right)\left(x^2+2xy-4y^2\right)-\left(x-2y\right)^3\)
\(=2x^3+4x^2y-8xy^2-x^2y-2xy^2+4y^3-x^3+6x^2y-12xy^2+8y^3\)
\(=x^3+9x^2y-22xy^2+12y^3\)