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a) Đặt 3x làm nhân tử chung ta được 3x( 8 x 4 + 3 x 2 + 6x).
Thực hiện phép chia được thương 8 x 4 - 3 x 2 + 6x.
b) Thực hiện phép chia từng đơn thức được kết quả 5 3 x 2 + 6 x + 13 2 .
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\(3x^2\left(a-b+c\right)+36xy\left(a-b+c\right)+108y^2\left(a-b+c\right)\)
\(=\left(a-b+c\right)\left(3x^2+36xy+108y^2\right)\)
\(=3\left(a-b+c\right)\left(x^2+12xy+36y^2\right)\)
\(=3\left(a-b+c\right)\left(x+6y\right)^2\)
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\(x^2-2xy+y^2-4m^2+4mn-n^2\)
\(=\left(x^2-2xy+y^2\right)-\left(4m^2-4mn+n^2\right)\)
\(=\left(x-y\right)^2-\left(2m-n\right)^2\)
\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)
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Đề phải là:
x3y + 12x2y2 + 36 xy3
= xy(x2 + 2.x.6y + 36y2)
=xy[x2 + 2. x . 6y + (6y)2]
= xy(x+6y)2
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e: \(x^2+6x+9-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
f: \(x^2-2x+7x-14\)
\(=x\left(x-2\right)+7\left(x-2\right)\)
=(x-2)(x+7)
h: \(5x^2-10xy+5y^2-20\)
\(=5\left(x^2-2xy+y^2-4\right)\)
\(=5\left(x-y-2\right)\left(x-y+2\right)\)
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a: \(3x^4-6x^3+2x^2=x^2\left(3x^2-6x+2\right)\)
b: \(x^3y+12x^2y+36xy=xy\left(x^2+12x+36\right)=xy\left(x+6\right)^2\)
c: \(x^3y-9xy^3=xy\left(x^2-9y^2\right)=xy\left(x-3y\right)\left(x+3y\right)\)
d: \(x^2y^2-2xy^2+y^2=y^2\left(x-1\right)^2\)
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\(81x^2y-27xy^2=27xy\left(3x-y\right)\)
\(2x^3+4x^2-6x=2x\left(x^2+2x-3\right)=2x\left(x+3\right)\left(x-1\right)\)
\(25x^2-10xy+30xy^2=5x\left(5x-2y+6y^2\right)\)
\(27x^3-36xy=9x\left(3x^2-4y\right)\)
\(15x^2+30xy+25xy^2=5x\left(3x+6y+5y^2\right)\)
\(81x^2y-27xy^2==27xy\left(3x-y\right);2x^3+4x^2-6x=2x\left(x^2+2x-3\right)=2x\left(x+3\right)\left(x-1\right);25x^2-10xy+30xy^2=5x\left(5x-2y+6y^2\right);27x^3-36xy=3x\left(9x^2-12y\right);15x^2+30xy+25xy^2=5x\left(3x+6y+5y^2\right)\)
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a) (5x - 3y)(x - 3y)(x + 3y).
b) 3(a – b + c) ( x + 6 y ) 2 .
c) (x-y-2m + n)(x-y + 2m-n)
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\(18x^2-36xy+18x^2-72z^2\)
\(=36x^2-36xy-72z^2\)
\(=36\left(x^2-xy-2z^2\right)\)