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a) \(\dfrac{2x-2y}{x^2-2xy+y^2}=\dfrac{2\left(x-y\right)}{\left(x-y\right)^2}=\dfrac{2}{x-y}\)
b) \(\dfrac{2-2a}{a^3-1}=-\dfrac{2-2a}{1-a^3}=-\dfrac{2\left(1-a\right)}{\left(1-a\right)\left(1+a+a^2\right)}=\dfrac{-2}{\left(1+a+a^2\right)}\)
c) \(\dfrac{x^2-6x+9}{x^2-8x+15}\)
\(=\dfrac{x^2-2.x.3+3^2}{x^2-3x-5x+15}\)
\(=\dfrac{\left(x-3\right)^2}{\left(x^2-3x\right)-\left(5x-15\right)}\)
\(=\dfrac{\left(x-3\right)^2}{x\left(x-3\right)-5\left(x-3\right)}\)
\(=\dfrac{\left(x-3\right)^2}{\left(x-3\right)\left(x-5\right)}\)
\(=\dfrac{x-3}{x-5}\)
d) \(\dfrac{x^4-2x^3}{2x^4-x^3}\)
\(=\dfrac{x^3\left(x-2\right)}{x^3\left(2x-1\right)}\)
\(=\dfrac{x-2}{2x-1}\)
a) ( 5x - y )( 25x2 + 5xy + y2 ) = ( 5x )3 - y3 = 125x3 - y3
b) ( x - 3 )( x2 + 3x + 9 ) - ( 54 + x3 ) = x3 - 33 - 54 - x3 = -27 - 54 = -81
c) ( 2x + y )( 4x2 - 2xy + y2 ) - ( 2x - y )( 4x2 + 2xy + y2 ) = ( 2x )3 + y3 - [ ( 2x )3 - y3 ]= 8x3 + y3 - 8x3 + y3 = 2y3
d) ( x + y )2 + ( x - y )2 + ( x + y )( x - y ) - 3x2 = x2 + 2xy + y2 + x2 - 2xy + y2 + x2 - y2 - 3x2 = y2
e) ( x - 3 )3 - ( x - 3 )( x2 + 3x + 9 ) + 6( x + 1 )2
= x3 - 9x2 + 27x - 27 - ( x3 - 33 ) + 6( x2 + 2x + 1 )
= x3 - 9x2 + 27x - 27 - x3 + 27 + 6x2 + 12x + 6
= -3x2 + 39x + 6
= -3( x2 - 13x - 2 )
f) ( x + y )( x2 - xy + y2 ) + ( x - y )( x2 + xy + y2 ) - 2x3
= x3 + y3 + x3 - y3 - 2x3
= 0
g) x2 + 2x( y + 1 ) + y2 + 2y + 1
= x2 + 2x( y + 1 ) + ( y2 + 2y + 1 )
= x2 + 2x( y + 1 ) + ( y + 1 )2
= ( x + y + 1 )2
= [ ( x + y ) + 1 ]2
= ( x + y )2 + 2( x + y ) + 1
= x2 + 2xy + y2 + 2x + 2y + 1
bài 1:
a) (x+1)^2-(x-1)^2-3(x+1)(x-1)
=(x+1+x-1)(x+1-x+1)-3x^2-3
=2x^2-3x^2-3
=-x^2-3