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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có
a, x2-x-y2-y
=x2-y2-(x+y)
=(x-y)(x+y) - (x+y)
=(x+y)(x-y-1)
b, x2-2xy+y2-z2
=(x-y)2-z2
=(x-y-z)(x-y+z)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
4x(x+y)(x+y+z)(x+z)+(yz)^2
=(2x(x+y+z))(2(x+y)(x+z)+(yz)^2
=(2x^2+2xy+2xz)(2x^2+2xy+2xz+2yz)+(yz)^2
Đặt t=C
=(t-yz)(t+yz)-(yz)^2
=t^2-(yz)^2+(yz)^2=t^2=(2x^2+2xy+2xz+yz)^2
=
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\(4x^2-y^2+8\left(y-2\right)=4x^2-y^2+8y-16=4x^2-\left(y-4\right)^2=\left(2x-y+4\right)\left(2x+y-4\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\((4x-y)(a+b)(4x-y)(c-1)\)
\(=\left(4x-y\right)\left(4x-y\right)=\left(4x-y\right)^{1+1}=\left(4y-2\right)^2\)
\(=\left(a+b\right)\left(4x-y\right)^2\left(c-1\right)\)
(4x-y)(a+b)(4x-y)(c-1)
= ( 4x - y ) ( 4x - y ) = ( 4x - y ) 1 + 1 = ( 4y - 2 ) 2
= (a + b ) ( 4x - y )2 ( c - 1 )
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lưu ý rằng ba điều kiện đầu tiên yếu tố như (x + 1) ^ 2, do đó chúng ta có:
x^2 + 2x + 1 - y^2 = (x + 1)^2 - y^2.
(x + 1)^2 - y^2 = [(x + 1) + y][(x + 1) - y], từ a^2 - b^2 = (a + b)(a - b)
= (x + y + 1)(x - y + 1).
1. = (x-2)^2 - y^2 = (x - 2 - y)(x-2+y)
2. = (x-y-x-y)(x-y+x+y) = 2(-y)2x = -4xy
1=-(y^6-x^2-4x)