phan tich da thuc thanh nhan tu (x2-x+2)+(x-2)
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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)
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-10\)
\(=\left(x^2+x+5\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+5\right)\left(x+2\right)\left(x-1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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x(x+2)(x^2+2x+2)+1 = (x^2+2x)(x^2+2x+1)+1
Đặt x^2+2x+1=y ta được:
(y-)(y+1)+1=y^2-1+1=y^2
= (x^2+2x+1)^2
= ( x + 1 )^4
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
x^2 + 7x -15
= x^2 + 7x +12,25 -27,25
= (x+3,5)^2 - 27, 25
= ( x+3,5 - \(\sqrt{27,25}\))(x+3,5+\(\sqrt{27,25}\))
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1+2x\right).\left(1-2x\right)-x.\left(x+2\right).\left(x-2\right)\))
\(=1-\left(2x\right)^2-x.x^2-2^2\)
\(=1-4x^2-x^3-4\)
Ko bt có đúng ko nữa
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\left(x.x-x+2\right)+\left(x-2\right)\)
\(=x\left(x-x+2-2\right)=x.0\)
=x2-x+2+x-2
=x2