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a) 4x2 - 5xy + y2 = 4x2 - 4xy - xy + y2 = 4x( x - y ) - y( x - y ) = ( x - y )( 4x - y )
b) x2 - 4xy + 3y2 = x2 - xy - 3xy + 3y2 = x( x - y ) - 3y( x - y ) = ( x - y )( x - 3y )
c) 9x2 + 6xy - 8y2 = 9x2 - 6xy + 12xy - 8y2 = 9x( x - 2/3y ) + 12y( x - 2/3y ) = ( x - 2/3y )( 9x + 12y )
d) 2x2 + 3xy - 5y2 = 2x2 - 2xy + 5xy - 5y2 = 2x( x - y ) + 5y( x - y ) = ( x - y )( 2x + 5y )
e) x2 - 35y2 - 2xy = x2 + 5xy - 7xy - 35y2 = x( x + 5y ) - 7y( x + 5y ) = ( x + 5y )( x - 7y )
f) 2x2 + 10xy + 8y2 = 2( x2 + 5xy + 4y2 ) = 2( x2 + xy + 4xy + 4y2 ) = 2[ x( x + y ) + 4y( x + y ) ] = 2( x + y )( x + 4y )
g) x2 - 10xy + 16y2 = x2 - 2xy - 8xy + 16y2 = x( x - 2y ) - 8y( x - 2y ) = ( x - 2y )( x - 8y )
h) 4x2 + 4xy - 15y2 = 4x2 - 6xy + 10xy - 15y2 = 4x( x - 3/2y ) + 10y( x - 2/3y ) = ( x - 2/3y )( 4x + 10y )
i) -7xy + 3x2 + 2y2 = 3x2 - xy - 6xy + 2y2 = 3x( x - 1/3y ) - 6y( x - 1/3y ) = ( x - 1/3y )( 3x - 6y )
j) 56y2 + 4x2 - 36xy = 4( x2 - 9xy + 14y2 ) = 4( x2 - 2xy - 7xy + 14y2 ) = 4[ x( x - 2y ) - 7y( x - 2y ) ] = 4( x - 2y )( x - 7y )
\(b,\left(5xy-x^2+y\right).\dfrac{2}{5xy^2}\)
\(=5xy.\dfrac{2}{5xy^2}-x^2.\dfrac{2}{5xy^2}+y.\dfrac{2}{5xy^2}\)
\(=\dfrac{2}{y}-\dfrac{2x}{5y^2}+\dfrac{2}{5xy}\)
\(c,\left(4x^3-3xy^2+2xy\right)\left(-\dfrac{1}{3x^2y}\right)\)
\(=4x^3.\left(\dfrac{-1}{3x^2y}\right)-3xy^2.\left(\dfrac{-1}{3x^2y}\right)+2xy\left(-\dfrac{1}{3x^2y}\right)\)\(=\dfrac{-x}{3y}+\dfrac{y}{x}-\dfrac{2}{3x}\)
a) \(x^3\left(3x^2-x-\dfrac{1}{2}\right)=3x^5-x^4-\dfrac{1}{2}x^3\)
b) \(\left(5xy-x^2+y\right)\dfrac{2}{5}xy^2=2x^2y^3-\dfrac{2}{5}x^3y^2+\dfrac{2}{5}xy^3\)
c) \(\left(4x^3-3xy^2+2xy\right)\left(-\dfrac{1}{3}x^2y\right)=\dfrac{-4}{3}x^5y+x^3y^3-\dfrac{2}{3}x^3y^2\)
\(Sửa:\left(9x^2y-6xy^2+5xy\right):3xy=3x-2y+\dfrac{5}{3}\)