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a,\(\frac{1}{5}x^2y\left(15xy^2-5y+3xy\right)=3x^3y^3-x^2y^2+\frac{3}{5}x^3y^2\)
b,\(5x^3-5x=5x\left(x^2-1\right)=5x\left(x-1\right)\left(x+1\right)\)
c, \(3x^2+5y-3xy-5x=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
1) 1/5x2y( 15xy2 - 5y + 3xy ) = 3x3y3 - x2y2 + 3/5x3y2
2) a) 5x3 - 5x = 5x( x2 - 1 ) = 5x( x2 - 12 ) = 5x( x - 1 )( x + 1 )
b) 3x2 + 5y - 3xy - 5x = ( 3x2 - 3xy ) + ( 5y - 5x )
= 3x( x - y ) + 5( y - x )
= 3x( x - y ) + 5[ -( x - y ) ]
= 3x( x - y ) - 5( x - y )
= ( 3x - 5 )( x - y )
b, 3x^2+5y-3xy-5x
=(3x^2-3xy)+(5y-5x)
=3x(x-y)+5(y-x)
=3x(x-y)-5(x-y)
=(x-y)(3x-5)
a: =5(x+y-2x^2-2y^2)
b: =3x(x-y)-5(x-y)
=(x-y)(3x-5)
a) \(x^2-xy+x-y=\left(x^2-xy\right)+\left(x-y\right)\)
\(=x\left(x-y\right)+\left(x-y\right)=\left(x+1\right)\left(x-y\right)\)
b) \(3x^2-3xy-5x+5y=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)=\left(3x-5\right)\left(x-y\right)\)
a, \(4y^2+1-4y=\left(2y\right)^2-2.2y.1+1^2=\left(2y-1\right)^2\)
b, \(3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(3x-5\right)\left(x-y\right)\)
c, \(x^2-2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)
a)x2-xy+x-y
=x(x-y)+(x-y)
=(x+1)(x-y)
b)3x2-3xy-5x+5y
=3x(x-y)-5(x-y)
=(3x-5)(x-y)
a ) \(x^2-xy+x-y\).
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right).\)
b ) \(3x^2-3xy-5x+5y\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
c) \(3x^2-6x+9y^2=3\left(x^2-2x+3y^2\right)\)
h) \(3y^2-3z^2+3x^2+6xy=3\left(x^2-z^2+x^2+2xy\right)\)
\(=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y+z\right)\left(x+y-z\right)\)
g) \(3x^2+5y-3xy-5x=\left(3x^2-3xy\right)+\left(5y-5x\right)=3x\left(x-y\right)+5\left(y-x\right)=\left(x-y\right)\left(3x-5\right)\)
\(x^2-xy+x-y\)
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-1\right)\left(x-y\right)\)
a, \(x^2-xy+x-y=x\left(x-y\right)+\left(x-y\right)=\left(x-y\right)\left(x+1\right).\)
\(b,3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)
\(3x^2-5y-3xy-5x\)
\(=\left(3x^2-3xy\right)-\left(5y-5x\right)\)
\(=3x\left(x-y\right)-5\left(y-x\right)\)
\(=3\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3-5\right)\)