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11) \(3x\left(x-1\right)+5\left(1-x\right)=\left(3x-5\right)\left(x-1\right)\)
12) \(2\left(2x-1\right)+3\left(1-2x\right)=1-2x\)
13) \(10x\left(x-y\right)-8y\left(y-x\right)=2\left(x-y\right)\left(5x+4y\right)\)
14) \(3x\left(y+2\right)-3\left(y+2\right)=3\left(x-1\right)\left(y+2\right)\)
15) \(x^2-y^2-2x+2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right)\)
1) 2x2 - 4x = 2x( x - 2 )
2) 3x - 6y = 3( x - 2y )
3) x2 - 3x = x( x - 3 )
4) 4x2 - 6x = 2x( x - 3 )
5) x3 - 4x = x( x2 - 4 ) = x( x - 2 )( x + 2 )
1) \(2x^2-4x=2x\left(x-2\right)\)
2) \(3x-6y=3\left(x-2y\right)\)
3) \(x^2-3x=x\left(x-3\right)\)
4) \(4x^2-6x=2x\left(2x-3\right)\)
5) \(x^3-4x=x\left(x-2\right)\left(x+2\right)\)
1.\(x^2-2x-4y^2-4y=\left(x+2y\right)\left(x-2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)
2.\(x^4+2x^3-4x-4=\left(x^2+2\right)\left(x^2-2\right)+2x\left(x^2-2\right)=\left(x^2-2\right)\left(x^2+2x-2\right)\)
3.\(3x^2-3y^2-2\left(x-y\right)^2=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\left(x-y\right)=\left(x-y\right)\left(3x+3y-2x+2y\right)\)\(=\left(x-y\right)\left(x+5y\right)\)
4.\(x^3-4x^2-9x+36=x^2\left(x-4\right)-9\left(x-4\right)=\left(x-3\right)\left(x+3\right)\left(x-4\right)\)
5.\(\left(x-1\right)\left(2x+1\right)+3\left(x-1\right)\left(x+2\right)\left(2x+1\right)=\left(x-1\right)\left(2x+1\right)\left(1+3x+6\right)\)\(=\left(x-1\right)\left(2x+1\right)\left(3x+7\right)\)
6.\(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)=3\left(2x+1\right)-\left(2x-5\right)\left(2x+1\right)\)\(=\left(2x+1\right)\left(3-2x-5\right)=\left(2x+1\right)\left(-2-2x\right)=-2\left(2x+1\right)\left(x+1\right)\)
7.\(\left(x-5\right)^2+\left(x+5\right)\left(x-5\right)+\left(x-5\right)\left(2x+1\right)=\left(x-5\right)\left(x-5+x+5+2x+1\right)\)\(=\left(x-5\right)\left(4x+1\right)\)
8.\(\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)=\left(3x-2\right)\left(3x-6\right)=3\left(3x-2\right)\left(x-2\right)\)
a) \(4x\left(a-b\right)+6xy\left(b-a\right)\)
\(=4x\left(a-b\right)-6xy\left(a-b\right)\)
\(=\left(4x-6xy\right)\left(a-b\right)\)
\(=2x\left(2-3y\right)\left(a-b\right)\)
1) \(3x\left(x-1\right)+5\left(x-1\right)\)
\(=\left(x-1\right)\left(3x+5\right)\)
2) \(4x(x-2y)-8y(2y-x)\)
\(=4x\left(x-2y\right)+8y\left(x-2y\right)\)
\(=\left(4x+8y\right)\left(x-2y\right)\)
\(=4\left(x+2y\right)\left(x-2y\right)\)
3) \(a^2\left(x-1\right)+b^2\left(1-x\right)\)
\(=a^2\left(x-1\right)-b^2\left(x-1\right)\)
\(=\left(a^2-b^2\right)\left(x-1\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(x-1\right)\)
4) \(3x\left(x-a\right)+4a\left(a-x\right)\)
\(=3x\left(x-a\right)-4a\left(x-a\right)\)
\(=\left(x-a\right)\left(3x-4a\right)\)
5) \(5x\left(x-y\right)^2+10y^2\left(y-x\right)^2\)
\(=5x\left(x-y\right)^2+10y^2\left(x-y\right)^2\)
\(=\left(5x+10y^2\right)\left(x-y\right)^2\)
\(=5\left(x+2y^2\right)\left(x-y\right)^2\)
6) \(3x\left(x-3\right)^2+9\left(3-x\right)^2\)
\(=3x\left(x-3\right)^2+9\left(x-3\right)^2\)
\(=\left(3x+9\right)\left(x-3\right)^2\)
\(=3\left(x+3\right)\left(x-3\right)^2\)
7) \(x\left(m-a\right)^2-y\left(a-m\right)^2\)
\(=x\left(a-m\right)^2-y\left(a-m\right)^2\)
\(=\left(x-y\right)\left(a-m\right)^2\)
8) \(6y^2\left(x-1\right)^2+9y\left(1-x\right)^2\)
\(=6y^2\left(x-1\right)^2+9y\left(x-1\right)^2\)
\(=\left(6y^2+9x\right)\left(x-1\right)^2\)
\(=3\left(2y^2+3x\right)\left(x-1\right)^2\)
#Ayumu
1: \(x\left(x-1\right)+\left(1+x\right)^2\)
\(=x^2-x+x^2+2x+1\)
\(=2x^2+x+1\)
Đa thức này ko phân tích được nha bạn
2: \(\left(x+1\right)^2-3\left(x+1\right)\)
\(=\left(x+1\right)\cdot\left(x+1\right)-\left(x+1\right)\cdot3\)
\(=\left(x+1\right)\left(x+1-3\right)\)
\(=\left(x+1\right)\left(x-2\right)\)
3: \(2x\cdot\left(x-2\right)-\left(x-2\right)^2\)
\(=2x\left(x-2\right)-\left(x-2\right)\cdot\left(x-2\right)\)
\(=\left(x-2\right)\left(2x-x+2\right)\)
\(=\left(x-2\right)\left(x+2\right)\)
4: \(3x\left(x-1\right)^2-\left(1-x\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^2\cdot\left(x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(3x+x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(4x-1\right)\)
5: \(3x\left(x+2\right)-5\left(x+2\right)^2\)
\(=\left(x+2\right)\cdot3x-\left(x+2\right)\cdot\left(5x+10\right)\)
\(=\left(x+2\right)\left(3x-5x-10\right)\)
\(=\left(-2x-10\right)\left(x+2\right)\)
\(=-2\left(x+5\right)\left(x+2\right)\)
6: \(4x\left(x-y\right)+3\left(y-x\right)^2\)
\(=4x\left(x-y\right)+3\left(x-y\right)^2\)
\(=\left(x-y\right)\cdot4x+\left(x-y\right)\left(3x-3y\right)\)
\(=\left(x-y\right)\cdot\left(4x+3x-3y\right)\)
\(=\left(x-y\right)\left(7x-3y\right)\)
Cảm ơn nhiều