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![](https://rs.olm.vn/images/avt/0.png?1311)
1) \(4x^5y^2-8x^4y^2+4x^3y^2\)
\(=4x^3y^2\left(x^2-2x+1\right)\)
\(=4x^3y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)
\(=4x^3y^2\left(x-1\right)^2\)
2) \(5x^4y^2-10x^3y^2+5x^2y^2\)
\(=5x^2y^2\left(x^2-2x+1\right)\)
\(=5x^2y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)
\(=5x^2y^2\left(x-1\right)^2\)
3) \(12x^2-12xy+3y^2\)
\(=3\left(4x^2-4xy+y^2\right)\)
\(=3\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=3\left(2x-y\right)^2\)
4) \(8x^3-8x^2y+2xy^2\)
\(=2x\left(4x^2-4xy+y^2\right)\)
\(=2x\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=2x\left(2x-y\right)^2\)
5) \(20x^4y^2-20x^3y^3+5x^2y^4\)
\(=5x^2y^2\left(4x^2-4xy+y^2\right)\)
\(=5x^2y^2\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=5x^2y^2\left(2x-y\right)^2\)
1: 4x^5y^2-8x^4y^2+4x^3y^2
=4x^3y^2(x^2-2x+1)
=4x^3y^2(x-1)^2
2: \(=5x^2y^2\left(x^2-2x+1\right)=5x^2y^2\left(x-1\right)^2\)
3: \(=3\left(4x^2-4xy+y^2\right)=3\left(2x-y\right)^2\)
4: \(=2x\left(4x^2-4xy+y^2\right)=2x\left(2x-y\right)^2\)
5: \(=5x^2y^2\left(4x^2-4xy+y^2\right)=5x^2y^2\left(2x-y\right)^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
giai phuong trinh
1, (x-2)(x-1)(x-8)(x-4)=4x^2
2, (x^2+5x+6)(x^2+20x+96)=4x^2
3, 3(x^2+2x-1)^2-2(x^2+3x-1)^2+5x^2=0
![](https://rs.olm.vn/images/avt/0.png?1311)
c \(\frac{\left(2x-4\right)\left(x-3\right)}{\left(x-2\right)\left(3x^2-27\right)}=\frac{2\left(x-2\right)\left(x-3\right)}{3\left(x-2\right)\left(x^2-9\right)}\)
\(=\frac{2\left(x-2\right)\left(x-3\right)}{3\left(x-2\right)\left(x-3\right)\left(x+3\right)}=\frac{2}{3\left(x+3\right)}\)
d, \(\frac{x^2+5x+6}{x^2+4x+4}=\frac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)^2}=\frac{x+3}{x+2}\)
Tương tự với a ; b
![](https://rs.olm.vn/images/avt/0.png?1311)
\(8x^2+6x^3=2x^2\left(4+3x\right)\)
\(x^3-5x^2-4x+20=x^2\left(x-5\right)-4\left(x-5\right)=\left(x^2-4\right)\left(x-5\right)=\left(x-2\right)\left(x+2\right)\left(x-5\right)\)
\(x^2-9y^2-4x+4=\left(x^2-4x+4\right)-\left(3y\right)^2=\left(x-2\right)^2-\left(3y\right)^2=\left(x-2-3y\right)\left(x-2+3y\right)\)
a: \(8x^2+6x^3=2x^2\left(4+3x\right)\)
b: \(x^3-5x^2-4x+20\)
\(=x^2\left(x-5\right)-4\left(x-5\right)\)
\(=\left(x-5\right)\left(x-2\right)\left(x+2\right)\)
c: \(x^2-4x+4-9y^2\)
\(=\left(x-2\right)^2-9y^2\)
\(=\left(x-2-3y\right)\left(x-2+3y\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
d: ta có: \(x^2-4x+4=9\left(x-2\right)\)
\(\Leftrightarrow\left(x-2\right)\left(x-11\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=11\end{matrix}\right.\)
\(4x\left(x^2-5x+3\right)=4x^3-20x^2+12x\)
=> Chọn A