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a) \(x^2-5x+5y-y^2\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
b) \(2\left(x^2+1\right)^2-8x^2\)
\(=2\left[\left(x^2+1\right)^2-4x^2\right]\)
\(=2\left(x^2-2x+1\right)\left(x^2+2x+1\right)\)
\(=2\left(x-1\right)^2\left(x+1\right)^2\)
\(4x^4-9x^2\)
\(=\left(2x^2\right)^2-\left(3x\right)^2\)
\(=\left(2x^2-3x\right)\left(2x^2+3x\right)\)
a)\(x^2-y^2-x-y=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
b)\(x^2-5x+5y-y^2=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
a) (x-y)(x+y)-(x+y)=(x+y)(x-y-1) b) (x^2-y^2)-(5x-5y)=(x-y)(x+y)-5(x+y)=(x+y)(x-y-5) c) (x^3+1)-3x(x+1)=(x+1)(x^2-x+1)-3x(x+1)=(x+1)(x^2-4x+1)
\(a,4x^4-8x^3+4x^2\)
\(=4x^2\cdot\left(x^2-2x+1\right)\)
\(=4x^2\cdot\left(x-1\right)^2\)
\(b,x^2-y^2+5\cdot\left(y-x\right)\)
\(=\left(x-y\right)\cdot\left(x+y\right)-5\cdot\left(x-y\right)\)
\(=\left(x-y\right)\cdot\left(x+y-5\right)\)
\(c,3x^2-6xy+3y^2-12z^2\)
\(=3\cdot\left(x^2-2xy+y^2-4x^2\right)\)
\(=3\cdot\left[\left(x-y\right)^2-\left(2x\right)^2\right]\)
\(=3\cdot\left(x-y-2x\right)\cdot\left(x-y+2x\right)\)
a) 2xy2 - 6x2y + 4xy
= 2xy.(y - 3x + 2)
b) x2 - y2 - 5x + 5y
= (x+y).(x-y) - 5.(x-y)
= (x-y).(x+y-5)
c) x2 - 4y2 - 1 + 4y
= x2 - (4y2 - 4y + 1)
= x2 - [ (2y)2 - 2.2.y.1 + 12 ]
= x2 - (2y-1)2
= (x+2y-1).(x-2y+1)
a) 4xn+2 + 8xn = 4xn( x2 + 2 )
b) ( 4x - 8 )( x2 + 6 ) - ( x - 2 )( x + 7 ) - 10 + 5x
= 4( x - 2 )( x2 + 6 ) - ( x - 2 )( x + 7 ) + 5( x - 2 )
= ( x - 2 )[ 4( x2 + 6 ) - ( x + 7 ) + 5 ]
= ( x - 2 )( 4x2 + 24 - x - 7 + 5 )
= ( x - 2 )( 4x2 - x + 22)
Phân tích các đa thức sau thành nhân tử :
a) x - y + 5x - 5y
= ( x + 5x ) - ( y + 5y )
= x . ( 1 + 6 ) - y . ( 1 + 6 )
= ( 1 + 6 ) . ( x - y )
\(a,x-y+5x-5y=\left(x-y\right)+5\left(x-y\right)=6\left(x-y\right)\)