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\(a)\) \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)\left(x+1\right)\)
\(=\)\(\left(x+1-x+1\right).\left[\left(x+1\right)^2+\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\right]-6\left(x^2-1\right)\)
\(=\)\(2\left(x^2+2x+1+x^2-1+x^2-2x+1\right)-6x^2+6\)
\(=\)\(2\left(3x^2+1\right)-6x^2+6\)
\(=\)\(6x^2+2-6x^2+6\)
\(=\)\(8\)
Chúc bạn học tốt ~
a) \(\frac{2x^3+x^2+x+6}{x^2-x+2}=\frac{\left(2x+3\right)\left(x^2-x+2\right)}{x^2-x+2}=2x+3\)
b) \(\frac{x}{x-3}-\frac{5x^2+27}{x^2-9}+\frac{x-9}{x+3}\)
\(=\frac{x}{x-3}-\frac{5x^2+27}{\left(x-3\right)\left(x+3\right)}+\frac{x-9}{x+3}\)
\(=\frac{x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{5x^2+27}{\left(x-3\right)\left(x+3\right)}+\frac{\left(x-9\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{x^2+3x}{\left(x-3\right)\left(x+3\right)}-\frac{5x^2+27}{\left(x-3\right)\left(x+3\right)}+\frac{x^2-12x+27}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{x^2+3x-\left(5x^2+27\right)+x^3-12x+27}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{-3x^2-9x}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{-3x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{-3x}{x-3}\)
a) ( x - 2 )3 - x( x + 1 )( x - 1 ) + 6x( x - 3 )
= x3 - 6x2 + 12x - 8 - x( x2 - 1 ) + 6x2 - 18x
= x3 - 6x - 8 - x3 + x
= -5x - 8
b) ( x + 1 )3 - ( x - 1 )3 - 6( x - 1 )2
= x3 + 3x2 + 3x + 1 - ( x3 - 3x2 + 3x - 1 ) - 6( x2 - 2x + 1 )
= x3 + 3x2 + 3x + 1 - x3 + 3x2 - 3x + 1 - 6x2 + 12x - 6
= 12x - 4
c) ( 2x + 1 )( 4x2 - 2x + 1 ) + ( 2 - 3x )( 4 + 6x + 9x2 ) - 9
= ( 2x )3 + 13 + 23 - ( 3x )3 - 9
= 8x3 + 1 + 8 - 27x3 - 9
= -19x3
d) ( x + 1 )3 + ( x - 1 )3 + x3 - 3x( x - 1 )( x + 1 )
= x3 + 3x2 + 3x + 1 + x3 - 3x2 + 3x - 1 + x3 - 3x( x2 - 1 )
= 3x3 + 6x - 3x2 + 3x
= 9x
\(a,\left(x+3\right).\left(x^2-3x+9\right)-\left(54+x^3\right)=x^3+27-54-x^3=-27.\)
\(b,8x^3+y^3-8x^3+y^3=2y^3\)
( x - 1)3 - (x + 3) . (x2 - 3x + 9) + 3 . (x + 2) - (x - 2) = 2
=>x3-3x2.(-1)+3x.(-1)2-(-1)3-x(x2-3x+9)-3(x2-3x+9)+3x+6-x+2=2
x3+3x2+3x+1-x3+3x2-9x-3x2+9x-27+3x+6-x+2=2
(x3-x3)+(3x2+3x2-3x2)+(3x-9x+9x+3x-x)+(1-27+6+2)=2
3x2-5x-18=2
x(3x-5)=20
Thử lần lượt nha bạn
Bài 2
(x+y+z)2-2(x+y+z)(x+y)+(x+y)2
=(x+y+z)2-2x2-4xy-2xz-2yz+x2+2.xy+y2
=z2+(y+x)2z+y2+2xy+x2-2x2-4xy-2z(x+y)+x2+2xy+y2
=z2+(x+y)2z-2z(x+y)+(y2+y2)+(2xy+2xy-4xy)+(x2-2x2+x2)
=z2+2y2
`(x-9)^2-(x+3)^2`
`=(x-9-x-3)(x-9+x+3)`
`=-12(2x-6)`
`=-24x+72`
(x - 9)2 - (x + 3)2
= (x - 9 - x - 3)(x - 9 + x + 3)
= -12(2x -6)
= -24 - 72