9x-15y (phân tích theo nhân tử chung)
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\(12x^2+20xy-9x-15y\)
\(=4x\left(3x+5y\right)-3\left(3x+5y\right)\)
\(=\left(4x-3\right)\left(3x+5y\right)\)
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1) \(5x^2-5xy-9x+9y\)
\(=5x\left(x-y\right)-9\left(x-y\right)\)
\(=\left(5x-9\right)\left(x-y\right)\)
2) \(m^3+4m^2+3m\)
\(=m^3+3m^2+m^2+3m\)
\(=m^2.\left(m+3\right)+m\left(m+3\right)\)
\(=\left(m^2+m\right)\left(m+3\right)\)
\(=m\left(m+1\right)\left(m+3\right)\)
3) \(x^2-2xy-15y^2\)
\(=x^2-2xy+y^2-16y^2\)
\(=\left(x-y\right)^2-\left(4y\right)^2\)
\(=\left(x-y-4y\right)\left(x-y+4y\right)\)
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\(9x^6-12x^7+4x^8\)
\(=x^6\left(4x^2-12x+9\right)\)
\(=x^6.\left(2x-3\right)^2\)
hk
tốt
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\(=-16x^4y^6-24x^5y^5-9x^6y^4\)
\(=-x^4y^4\left(3x+4y\right)^2\)
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= (x - y).(x + y) - (15x - 15y)
= (x - y).(x + y) - 15.(x - y)
(x - y).(x + y -15)
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Phân tích đa thức thành nhân tử bằng phương pháp đặt nhân tử chung
(3x + 2)^2 + (3x - 2)^2 - 2(9x^2 - 4)
\(=\left(3x+2\right)^2-2\left(3x+2\right)\left(3x-2\right)+\left(3x-2\right)^2\)
\(=\left(3x+2-\left(3x-2\right)\right)^2\)
\(=\left(3x+2-3x+2\right)^2\)
\(=4^2\)
\(=16\)
\(\left(3x+2\right)^2+\left(3x-2\right)^2-2\left(9x^2-4\right)\)
\(=\left(3x+2\right)^2+\left(3x-2\right)^2-2.\left(3x-2\right)\left(3x+2\right)\)
\(=\left(3x+2-3x+2\right)^2\)
\(=4^2=16\)
![](https://rs.olm.vn/images/avt/0.png?1311)
x2-8xy+15y2 +2x-4y-3
= (x-4y)2 - y2 + (2x-8y) +4y -3
= (x-4y)2 +2(x-4y) +1 - y2+4y-4
= (x-4y+1)2 -(y-2)2 = (x-3y-1)(y-5y+3)
9x - 15y = 3 . 3x - 3 . 5y
= 3 . ( 3x - 5y )