a, \(x^2-x-y^2-y\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+1\right)\left(x-y-1\right)\)
b, \(a^3-a^2x-ay+xy\)
\(=a^2\left(a-x\right)-y\left(a-x\right)=\left(a^2-y\right)\left(a-x\right)\)
c, sai đề?
d, \(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
a ) \(x^2-x-y^2-y=\left(x^2-x\right)-\left(y^2+y\right)=x\left(x-1\right)-y\left(y+1\right)\)
c ) \(5x^2-10xy+5y^2-20z^2\)
\(=5\left(x^2-2xy+y^2\right)-20z^2\)
\(=5\left(x-y\right)^2-20z^2\)
\(=5\left[\left(x-y\right)^2-4z^2\right]\)
\(=5\left(x-y+2z\right)\left(x-y-2z\right)\)
d ) \(x^3-x+3x^2y+3xy^2+y^3-y=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
a, x2 - x - y2 - y = ( x - y ) ( x + y ) - ( x + y )
= ( x + y )( x - y - 1 )
b, a3 - a2x - ay + xy = a2( a - x ) - y( a - x )
= ( a2 - y )( a - x )
c, 5x2 - 10xy + 5x2 - 20z2 = 5 ( 2x2 - 2xy - 4z2 )
d, x3− x + 3x2y + 3xy2 + y3 − y
= ( x + y )3 - ( x + y )
= ( x + y )\([\) ( x + y )2 - 1 \(]\)
= ( x + y )( x + y +1 )( x + y - 1 )
