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\(b,2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x+1+y\right)\left(x+1-y\right)\)
a) x3 + 2x2y + xy2– 9x = x(x2 +2xy + y2 – 9)
= x[(x2 + 2xy + y2) – 9]
= x[(x + y)2 – 32]
= x(x + y – 3)(x + y + 3)
b) 2x – 2y – x2 + 2xy – y2 = (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)[2 – (x – y)]
= (x – y)(2 – x + y)
c) x4 – 2x2 = x2(x2 – (√2)2) = x2(x - √2)(x + √2).
a) 36 - 4a2 + 20ab - 25b2 = 36 - ( 4a2 - 20ab + 25b2 ) = 62 - ( 2a - 5b )2 = ( 6 - 2a + 5b )( 6 + 2a - 5b )
b) ( xy + 4 )2 - 4( x + y )2 = ( xy + 4 )2 - 22( x + y )2 = ( xy + 4 )2 - [ 2( x + y ) ]2
= ( xy + 4 )2 - ( 2x + 2y )2 = ( xy + 4 - 2x - 2y )( xy + 4 + 2x + 2y )
= [ x( y - 2 ) - 2( y - 2 ) ][ x( y + 2 ) + 2( y + 2 ) ]
= ( y - 2 )( x - 2 )( y + 2 )( x + 2 )
c) x2 + y2 - x2y2 + xy - x - y
= ( x2 - x2y2 ) + ( y2 - y ) + ( xy - x )
= x2( 1 - y2 ) + y( y - 1 ) + x( y - 1 )
= x2( 1 - y )( 1 + y ) - y( 1 - y ) - x( 1 - y )
= ( 1 - y )[ x2( 1 + y ) - y - x ) ]
= ( 1 - y )( x2 + x2y - y - x )
= ( 1 - y )[ ( x2 - x ) + ( x2y - y ) ]
= ( 1 - y )[ x( x - 1 ) + y( x2 - 1 ) ]
= ( 1 - y )[ x( x - 1 ) + y( x - 1 )( x + 1 ) ]
= ( 1 - y )( x - 1 )[ x + y( x + 1 ) ]
= ( 1 - y )( x - 1 )( x + xy + y )
d) 3x + 3y - x2 - 2xy - y2
= 3( x + y ) - ( x2 + 2xy + y2 )
= 3( x + y ) - ( x + y )2
= ( x + y )( 3 - x - y )
e) ( 2xy + 1 )2 - ( 2x + y )2
= ( 2xy + 1 - 2x - y )( 2xy + 1 + 2x + y )
= [ ( 2xy - 2x ) - ( y - 1 ) ][ ( 2xy + 2x ) + ( y + 1 ) ]
= [ 2x( y - 1 ) - ( y - 1 ) ][ 2x( y + 1 ) + ( y + 1 ) ]
= ( y - 1 )( 2x - 1 )( y + 1 )( 2x + 1 )
a) \(36-4a^2+20ab-25b^2\)
\(=36-\left(4a^2-20ab+25b^2\right)\)
\(=36-\left(2a-5b\right)^2\)
\(=\left(6-2a+5b\right)\left(6+2a-5b\right)\)
b) \(\left(xy+4\right)^2-4\left(x+y\right)^2\)
\(=\left(xy+4-2x-2y\right)\left(xy+4+2x+2y\right)\)
\(=\left[x\left(y-2\right)-2\left(y-2\right)\right]\left[x\left(y+2\right)+2\left(y+2\right)\right]\)
\(=\left(x+2\right)\left(x-2\right)\left(y+2\right)\left(y-2\right)\)
c) \(x^2+y^2-x^2y^2+xy-x-y\)
\(=-\left(x^2y^2-x^2\right)+\left(y^2-y\right)+\left(xy-x\right)\)
\(=-x^2\left(y-1\right)\left(y+1\right)+y\left(y-1\right)+x\left(y-1\right)\)
\(=\left(y-1\right)\left(-x^2y-x^2+y+x\right)\)
\(=\left(1-y\right)\left[\left(x^2y-y\right)+\left(x^2-x\right)\right]\)
\(=\left(1-y\right)\left(x-1\right)\left(xy+y+x\right)\)
1) Ta có: 2xy - x2 - y2 + 16
= -(x2 - 2xy + y2 - 16)
= -[(x - y)2 - 16]
= -(x - y - 4)(x - y + 4)
2) x3 + 2x2y + xy2 - 9x
= x(x2 + 2xy + y2 - 9)
= x[(x + y)2 - 9]
= x(x + y - 3)(x + y + 3)
3) x4 - 2x2 = x2(x2 - 2)
1. 2xy-x2-y2+16= -(x2-2xy+y2-16) = -(x2-2xy+y2)-16 = -(x-y)2-16= (x+y)2-42= (x+y-4).(x+y+4)
2. x3+2x2y+xy2-9x= (có sai đề không vậy?)
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a) =(2x+3y-1)2
b)=-(x-1)3
c)=-(x3-6x2+12x-8)=-(x-2)3
d)x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 -9)
= x[(x2 + 2xy + y2) - 32]
= x[(x + y)2 - 32]
= x (x + y – 3)(x + y + 3)
e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)
1, x2(x2+2x+1)=x2(x+1)2
2, 2(x2+2x+1-y2)=2(x+1-y)(x+1+y)
3, 16-(x2+2xy+y2)=(4-x-y)(4+x+y)
\(x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
hk tốt
^^
1/ x(y+2) -2(y+2)=(y+2)(x-2)
2/ 2(x-y) - (x-y)2 = (x-y)(2-x+y)
a) \(x^3+2x^2y+xy^2-9x\)
\(=x\left(x+y\right)^2-9x\)
\(=x\left(x+y-3\right)\left(x+y+3\right)\)
b) \(2x-2y-x^2+2xy-y^2=2\left(x-y\right)-\left(x-y\right)^2=\left(x-y\right)\left(2-x+y\right)\)
c) \(x^4-2x^2=x^2\left(x^2-2\right)\)