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1. Ta có : 2x4 - 3x3 - 3x2 + 6x - 2
= 2x4 - 2x3 - x3 + x2 - 4x2 + 4x + 2x - 2
= 2x3( x - 1 ) - x2( x - 1 ) - 4x( x - 1 ) + 2( x - 1 )
= ( x - 1 )( 2x3 - x2 - 4x + 2 )
= ( x - 1 )[ x2( 2x - 1 ) - 2( 2x - 1 ) ]
= ( x - 1 )( 2x - 1 )( x2 - 2 )
=> ( 2x4 - 3x3 - 3x2 + 6x - 2 ) : ( x2 - 2 ) = ( x - 1 )( 2x - 1 ) = 2x2 - 3x + 1
2. \(\left(15x^4y^6-12x^3y^4-18x^2y^3\right)\div\left(-6x^2y^2\right)\)
\(=\frac{15x^4y^6}{-6x^2y^2}-\frac{12x^3y^4}{-6x^2y^2}-\frac{18x^2y^3}{-6x^2y^2}\)
\(=-\frac{5}{2}x^2y^4+2xy^2+3y\)
Thực hiện phép tính
\(\left(15x^4y^6-12x^3y^4-18x^2y^3\right)\): \(\left(-6x^2y^2\right)\)
\(=\dfrac{-5}{2}x^2y^3+2xy^2+3y\)
a) \(\dfrac{6x^2y^3-2x^2y+6xy}{6xy}\)
\(=\dfrac{6x^2y^3}{6xy}-\dfrac{2x^2y}{6xy}+\dfrac{6xy}{6xy}\)
\(=xy^2-\dfrac{x}{3}+1\)
b) \(\dfrac{4\left(x+y\right)^3}{2\left(x+y\right)}\)
\(=\dfrac{2\left(x+y\right).2\left(x+y\right)^2}{2\left(x+y\right)}\)
\(=2\left(x+y\right)^2\)
c) \(\dfrac{8x^3+27y^3}{2x+3y}\)
\(=\dfrac{\left(2x\right)^3+\left(3y\right)^3}{2x+3y}\)
\(=\dfrac{\left(2x+3y\right)\left[\left(2x\right)^2-2x.3y+\left(3y\right)^2\right]}{2x+3y}\)
\(=4x^2-6xy+9y^2\)
d) \(\dfrac{48x^4y^3-12x^2y^5+6x^2y^2}{3x^2y^2}\)
\(=\dfrac{48x^4y^3}{3x^2y^2}-\dfrac{12x^2y^5}{3x^2y^2}+\dfrac{6x^2y^2}{3x^2y^2}\)
\(=16x^2y-4y^3+2\)
Bài làm
a, \(2x^2\left(3x-5\right)=6x^3-10x^2\)
b, \(\left(12x^3y^2-18x^2y\right):2xy=\left(12x^3y^2:2xy\right)-\left(18x^2y:2xy\right)=6x^2y-9x\)
\(=3x^2y+4xy-2x\)
\(\dfrac{-18x^4y^3-24x^3y^4+12x^3y^3}{-6x^2y^3}\)
\(=3x^2+4xy-2x\)