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`#3107.101107`
`x^2 - y^2 + 10x - 10y`
`= (x^2 - y^2) + (10x - 10y)`
`= (x - y)(x + y) + 10(x - y)`
`= (x + y + 10)(x - y)`
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Sử dụng HĐT:
`A^2 - B^2 = (A - B)(A + B).`
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\(x^2-y^2+10x-6y+16\)
\(=\left(x^2+10x+25\right)-\left(y^2+6y+9\right)\)
\(=\left(x+5\right)^2-\left(y+3\right)^2\)
\(=\left(x+5-y-3\right)\left(x+5+y+3\right)\)
\(=\left(x-y+2\right)\left(x+y+8\right)\)
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a) \(x^2-3x=x\left(x-3\right)\)
b) \(10x\left(x-y\right)-8y\left(x-y\right)=2\left(x-y\right)\left(5x-4y\right)\)
c) \(x^2-9=\left(x-3\right)\left(x+3\right)\)
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\(10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+8y\right)\)
\(=2\left(x-y\right)\left(5x+4y\right)\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt x2+10x+5=a.Ta có biểu thức là : a(a+8)+16=a2+8a+16=(a+4)2=(x2+10x+9)2