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a) \(x^4-2x^2+1=\left(x^2-1\right)^2=\left(x-1\right)^2\left(x+1\right)^2\)
b) \(x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)
c) \(2x^3-x^2-8x+4\)
\(=x^2\left(2x-1\right)-4\left(2x-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(2x-1\right)\)
d) \(x\left(x-y\right)^2+y\left(x-y\right)^2-xy+x^2\)
\(=\left(x+y\right)\left(x-y\right)^2+x\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2+x\right)\)
e) \(2x^2-5x+2\)
\(=\left(2x^2-x\right)-\left(4x-2\right)\)
\(=x\left(2x-1\right)-2\left(2x-1\right)\)
\(=\left(x-2\right)\left(2x-1\right)\)
a) ( 3x - 2 )( 4x + 5 ) - 6x( 2x - 1 )
= 12x2 + 7x - 10 - 12x2 + 6x
= 13x - 10
b) ( 2x - 5 )2 - 4( x + 3 )( x - 3 )
= 4x2 - 20x + 25 - 4( x2 - 9 )
= 4x2 - 20x + 25 - 4x2 + 36
= 61 - 20x
c) 2x3 - 5x2 + 7x - 6
= 2x3 - 3x2 - 2x2 + 3x + 4x - 6
= x2( 2x - 3 ) - x( 2x - 3 ) + 2( 2x - 3 )
= ( 2x - 3 )( x2 - x + 2 )
=> ( 2x3 - 5x2 + 7x - 6 ) : ( 2x - 3 ) = x2 - x + 2
a, (3x - 2 ) (4x + 5) - 6x (2x -1) = ( 7x + 15x -8x - 10 ) - ( 12x2 -6x ) = 7x2 + 15x - 8x -10 -12x2 + 6x = -5x2 + x - 10
a, \(\left(x+1\right)\left(x-2\right)=x^2-2x+x-2=x^2-x-2\)
b, \(-7x^2\left(3x-4y\right)=-21x^3+28x^2y\)
c, \(\left(x+4\right)\left(x-2\right)-\left(x-3\right)^2=x^2-2x+4x-8-\left(x^2-6x+9\right)\)
\(=x^2+2x-8-x^2+6x-9=8x-17\)
a: \(=6x^3-12x^2+x^2-2x+x-2\)
\(=\left(x-2\right)\left(6x^2+x+1\right)\)
b: \(=3x^4+3x^3-x^3-x^2-7x^2-7x+5x+5\)
\(=\left(x+1\right)\left(3x^3-x^2-7x+5\right)\)
\(=\left(x+1\right)\left(3x^3-3x^2+2x^2-2x-5x+5\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(3x^2+2x-5\right)\)
\(=\left(x-1\right)^2\cdot\left(x+1\right)\left(3x+5\right)\)
c: \(=4x^3+x^2+4x^2+x+4x+1\)
\(=\left(4x+1\right)\left(x^2+x+1\right)\)
a) \(2x\left(3x^2-5x+3\right)\)
\(=6x^3-10x^2+6x\)
b) \(-2x\left(x^2+5x-3\right)\)
\(=-2x^3-10x^2+6x\)
c) \(\frac{-1}{2}x^2\left(2x^3-4x+3\right)\)
\(=-x^5+2x^3-\frac{3}{2}x^2\)
a) 2x(3x2-5x+3)= 6x3-10x2+6x
b) -2x(x2+5x-3)= -4x3-10x2+6x
c) -1/2x2(2x3-4x+3)= -x5+2x2-3/2x
\(=2x.x-2x.3+x-3\\ =2x^2-6x+x-3\\ =2x^2-5x-3\)
=> Chọn B