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a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
a) 5x3 - 40 = 5( x3 - 8 ) = 5( x - 2 )( x2 + 2x + 4 )
b) x2z + 4xyz + 4y2z = z( x2 + 4xy + 4y2 ) = z( x + 2y )2
c) 4x2 - y2 - 6x + 3y = ( 4x2 - y2 ) - ( 6x - 3y ) = ( 2x - y )( 2x + y ) - 3( 2x - y ) = ( 2x - y )( 2x + y - 3 )
d) x2 + 2x - 4y2 + 1 = ( x2 + 2x + 1 ) - 4y2 = ( x + 1 )2 - ( 2y )2 = ( x - 2y + 1 )( x + 2y + 1 )
e) 3x2 - 3y2 - 12x + 12y = 3( x2 - y2 - 4x + 4y ) = 3[ ( x2 - y2 ) - ( 4x - 4y ) ] = 3[ ( x - y )( x + y ) - 4( x - y ) ] = 3( x - y )( x + y - 4 )
f) x3 + 5x2 + 4x + 20 = x2( x + 5 ) + 4( x + 5 ) = ( x + 5 )( x2 + 4 )
g) x3 - x2 - 25x + 25 = x2( x - 1 ) - 25( x - 1 ) = ( x - 1 )( x2 - 25 ) = ( x - 1 )( x - 5 )( x + 5 )
a) \(5x^3-40=5\left(x^3-8\right)=5\left(x-2\right)\left(x^2+2x+4\right)\)
b) \(x^2z+4xyz+4y^2z=z\left(x^2+4xy+4y^2\right)=z\left(x+2y\right)^2\)
c) \(4x^2-y^2-6x+3y=\left(4x^2-y^2\right)-\left(6x-3y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)-3\left(2x-y\right)=\left(2x-y\right)\left(2x+y-3\right)\)
d) \(x^2+2x-4y^2+1=x^2+2x+1-4y^2\)
\(=\left(x+1\right)^2-4y^2=\left(x+2y+1\right)\left(x-2y+1\right)\)
e) \(3x^2-3y^2-12x+12y=3\left(x^2-y^2-4x+4y\right)\)
\(=3\left[\left(x^2-y^2\right)-\left(4x-4y\right)\right]=3\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]\)
\(=3\left(x-y\right)\left(x+y+4\right)\)
f) \(x^3+5x^2+4x+20=\left(x^3+5x^2\right)+\left(4x+20\right)\)
\(=x^2.\left(x+5\right)+4\left(x+5\right)=\left(x^2+4\right)\left(x+5\right)\)
g) \(x^3-x^2-25x+25=\left(x^3-x^2\right)-\left(25x-25\right)\)
\(=x^2\left(x-1\right)-25\left(x-1\right)=\left(x-1\right)\left(x^2-25\right)\)
\(=\left(x-1\right)\left(x-5\right)\left(x+5\right)\)
a) \(2x-6y=2\left(x-3y\right)\)
b) \(x^2-y^2=\left(x-y\right)\left(x+y\right)\)
c) \(2x^3+4x^2+2x=2x\left(x^2+2x+1\right)=2x\left(x+1\right)^2\)
d) \(x^2-2xy+y^2-9\)
\(=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
e) \(x^3-10x^2+25x=x\left(x^2-10x+25\right)=x\left(x-5\right)^2\)
f) \(xy+y^2-x-y=y\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(y-1\right)\)
a. 2x - 6y
Bài làm
a. 2x - 6y
= 2(x - 3y)
b. x2 - y2
= (x - y)(x + y)
c. 2x3 + 4x2 + 2x
= 2x(x2 + 2 + 1)
= 2x(x2 + 3)
d. x2 - 2xy + y2 - 9
= (x2 - 2xy + y2) - 9
= (x - y)2 - 9
= (x - y - 3)(x - y + 3)
e. x3 - 10x2 + 25x
= x(x2 - 10x + 25)
= x(x2 - 2.5.x + 52)
= x(x + 5)2
f. xy + y2 - x - y
= y(x + y) - (x + y)
= (x + y)(y - 1)
a) 2x - 6y = 2( x - 3y )
b) x2 - y2 = ( x - y )( x + y )
c) 2x3 + 4x2 + 2x = 2x( x2 + 2x + 1 ) = 2x( x + 1 )2
d) x2 - 2xy + y2 = ( x2 - 2xy + y2 ) - 9 = ( x - y )2 - 32 = ( x - y - 3 )( x - y + 3 )
e) x3 - 10x2 + 25x = x( x2 - 10x + 25 ) = x( x - 5 )2
f) xy + y2 - x - y = ( xy + y2 ) - ( x + y ) = y( x + y ) - ( x + y ) = ( x + y )( y - 1 )
a) \(7x^3y-3xyz-21x^2+9z\)
\(=7x^2\left(xy-3\right)-3z\left(xy-3\right)\)
\(=\left(7x^2-3z\right)\left(xy-3\right)\)
b) \(4x^2-2x-y^2-y\)
\(=\left[\left(2x\right)^2-y^2\right]-\left(2x+y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)-\left(2x+y\right)\)
\(=\left(2x+y\right)\left(2x-y-1\right)\)
c) \(9x^2-25y^2-6x+10y\)
\(=\left(3x\right)^2-\left(5y\right)^2-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y\right)-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y-2\right)\)
d) \(\left(5x-4\right)^2+\left(16-25x^2\right)+\left(5x-4\right)\left(3x+2\right)\)
\(=\left(5x-4\right)\left[\left(5x-4\right)+\left(3x+2\right)\right]+\left(4^2-\left(5x\right)^2\right)\)
\(=\left(5x-4\right)\left(8x-2\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left(2-8x\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left[\left(2-8x\right)+\left(4+5x\right)\right]\)
\(=\left(4-5x\right)\left(6-3x\right)\)
giúp mk với mọi người ơi
a) 4x3 + 4x2 + 6x
= 2x( 2x2 + 2x + 3 )
b) x3 + 4x2 - 29x + 24
= x3 + 8x2 - 4x2 - 32x + 3x + 24
= ( x3 - 4x2 + 3x ) + ( 8x2 - 32x + 24 )
= x( x2 - 4x + 3 ) + 8( x2 - 4x + 3 )
= ( x2 - 4x + 3 )( x + 8 )
= ( x2 - x - 3x + 3 )( x + 8 )
= [ x( x - 1 ) - 3( x - 1 ) ]( x + 8 )
= ( x - 1 )( x - 3 )( x + 8 )
c) x3 + 21x2 + 134x + 240
= x3 + 10x2 + 11x2 + 110x + 24x + 240
= ( x3 + 11x2 + 24x ) + ( 10x2 + 110x + 240 )
= x( x2 + 11x + 24 ) + 10( x2 + 11x + 24 )
= ( x + 10 )( x2 + 11x + 24 )
= ( x + 10 )( x2 + 3x + 8x + 24 )
= ( x + 10 )[ x( x + 3 ) + 8( x + 3 ) ]
= ( x + 10 )( x + 8 )( x + 3 )
d) 25x3 - 25x2y - x + y
= 25x2( x - y ) - 1( x - y )
= ( x - y )( 25x2 - 1 )
= ( x - y )( 5x - 1 )( 5x + 1 )
e) 2x5y - 4x3y + 2xy
= 2xy( x4 - 2x2 + 1 )
Đặt t = x2
= 2xy( t2 - 2t + 1 )
= 2xy( t - 1 )2
= 2xy( x2 - 1 )2
= 2xy[ ( x - 1 )( x + 1 ) ]2
= 2xy( x - 1 )2( x + 1 )2
g) x3 - 3x + 2
= x3 + 2x2 - 2x2 - 4x + x + 2
= ( x3 - 2x2 + x ) + ( 2x2 - 4x + 2 )
= x( x2 - 2x + 1 ) + 2( x2 - 2x + 1 )
= ( x + 2 )( x2 - 2x + 1 )
= ( x + 2 )( x - 1 )2