( 4x - 1 )³ - ( 4x - 3 )( 16x² + 3 )

= ( 4x )³ - 3.( 4x )².1 + 3.4x.1² - 1³ - ( 64x³ + 12x - 48x² - 9 )

= 64x³ - 48x² + 12x - 1 - 64x³ - 12x + 48x² + 9

= ( 64x³ - 64x³ ) + ( 48x² - 48x² ) + ( 12x - 12x ) + ( 9 - 1 )

= 8

a,\(\left(4x-1\right)^3-\left(4x-3\right)\left(16x^2+3\right)\)

\(=64x^3-48x^2+12x-1-64x^3-12x+48x^2+9\)

\(=8\)

\(\left(\frac{x^2-1}{x^4-x^2+1}-\frac{1}{x^2+1}\right)\times\left(x^4+\frac{1-x^4}{1+x^2}\right)\)

ĐK : ...

\(=\left(\frac{\left(x^2-1\right)\left(x^2+1\right)}{\left(x^4-x^2+1\right)\left(x^2+1\right)}-\frac{x^4-x^2+1}{\left(x^4-x^2+1\right)\left(x^2+1\right)}\right)\times\left(x^4+\frac{\left(1-x^2\right)\left(1+x^2\right)}{\left(1+x^2\right)}\right)\)

\(=\left(\frac{x^4-1}{\left(x^4-x^2+1\right)\left(x^2+1\right)}-\frac{x^4-x^2+1}{\left(x^4-x^2+1\right)\left(x^2+1\right)}\right)\times\left(x^4+1-x^2\right)\)

\(=\left(\frac{x^4-1-x^4+x^2-1}{\left(x^4-x^2+1\right)\left(x^2+1\right)}\right)\times\left(x^4-x^2+1\right)\)

\(=\frac{x^2-2\left(x^4-x^2+1\right)}{\left(x^4-x^2+1\right)\left(x^2+1\right)}\)

\(=\frac{x^2-2}{x^2+1}\)

Mình sửa dòng 5 một chút nhé 

\(=\frac{\left(x^2-2\right)\left(x^4-x^2+1\right)}{\left(x^4-x^2+1\right)\left(x^2+1\right)}\)( như kia dễ bị nhầm )

( 2x + 3 )( 4x² - 6x + 9 ) - 2( 4x³ - 1 )

= ( 2x )³ + 3³ - 8x³ + 2

= 8x³ + 27 - 8x³ + 2

= 29

[2x+3][4x2L- 6X+9L] - 2L[4x3l -1]

=[2xl]3l + 3l3 - 8x3l +2

=8x3l+27-8x3l +2 

= 29ll= 29l = 29

( x + 3 )( x - 3 ) - ( x + 5 )( x - 1 ) - ( x - 4 )²

= x² - 9 - ( x² + 4x - 5 ) - ( x² - 8x + 16 )

= x² - 9 - x² - 4x + 5 - x² + 8x - 16

= -x² + 4x - 20

= x^2 - 3^2 - ( x^2 + 4x - 5 ) - ( x^2 - 8x + 16 ) 

= x^2 - 9 - x^2 - 4x + 5 - x^2 +8x - 16 

= -x^2 + 4x - 20 

a) 2x( x - 7 ) - ( x + 3 )( x - 2 ) - ( x + 4 )( x - 4 )

= 2x² - 14x - ( x² + x - 6 ) - ( x² - 16 )

= 2x² - 14x - x² - x + 6 - x² + 16

= 22 - 15x

b) ( 2x + 5 )( x - 2 ) - 3( x + 2 )² + ( x + 1 )²

= 2x² + x - 10 - 3( x² + 4x + 4 ) + x² + 2x + 1

= 3x² + 3x - 9 - 3x² - 12x - 12

= -9x - 21

c) ( x + 3 )( x - 3 ) - ( x + 5 )( x - 1 ) - ( x - 4 )²

= x² - 9 - ( x² + 4x - 5 ) - ( x² - 8x + 16 )

= x² - 9 - x² - 4x + 5 - x² + 8x - 16

= -x² + 4x - 20

d) 2x( x + 1 )² - ( x - 1 )³ - ( x - 2 )( x² + 2x + 4 ) 

= 2x( x² + 2x + 1 ) - ( x³ - 3x² + 3x - 1 ) - ( x³ - 8 )

= 2x³ + 4x² + 2x - x³ + 3x² - 3x + 1 - x³ + 8

= 7x² - x + 9

e) ( x + 5 )( x - 5 )( x + 2 ) - ( x + 2 )³

= ( x² - 25 )( x + 2 ) - ( x³ + 6x² + 12x + 8 )

= x³ + 2x² - 25x - 50 - x³ - 6x² - 12x - 8

= -4x² - 37x - 58

kokokokokokoko biết

a) ( 4x² - 3x - 18 )² - ( 4x² + 3x )²

= [ ( 4x² - 3x - 18 ) - ( 4x² + 3x ) ][ ( 4x² - 3x - 18 ) + ( 4x² + 3x ) ]

= ( 4x² - 3x - 18 - 4x² - 3x )( 4x² - 3x - 18 + 4x² + 3x )

= ( -6x - 18 )( 8x² - 18 )

= -6( x + 3 ).2( 4x² - 9 )

= -12( x + 3 )( 2x - 3 )( 2x + 3 )

b) 9( x + y - 1 )² - 4( 2x + 3y + 1 )²

= 3²( x + y - 1 )² - 2²( 2x + 3y + 1 )²

= [ 3( x + y - 1 ) ]² - [ 2( 2x + 3y + 1 ) ]²

= ( 3x + 3y - 3 )² - ( 4x + 6y + 2 )²

= [ ( 3x + 3y - 3 ) - ( 4x + 6y + 2 ) ][ ( 3x + 3y - 3 ) + ( 4x + 6y + 2 ) ]

= ( 3x + 3y - 3 - 4x - 6y - 2 )( 3x + 3y - 3 + 4x + 6y + 2 )

= ( -x - 3y - 5 )( 7x + 9y - 1 )

c) -4x² + 12xy - 9y² + 25

= 25 - ( 4x² - 12xy + 9y² )

= 5² - ( 2x - 3y )²

= [ 5 - ( 2x - 3y ) ][ 5 + ( 2x - 3y ) ]

= ( 5 - 2x + 3y )( 5 + 2x - 3y )

d) x² - 2xy + y² - 4m² + 4mn - n²

= ( x² - 2xy + y² ) - ( 4m² - 4mn + n² )

= ( x - y )² - ( 2m - n )²

= [ ( x - y ) - ( 2m - n ) ][ ( x - y ) + ( 2m - n ) ]

= ( x - y - 2m + n )( x - y + 2m - n )

a) ( xy + 1 )² - ( x + y )²

= [ ( xy + 1 ) - ( x + y ) ][ ( xy + 1 ) + ( x + y ) ]

= ( xy - x - y + 1 )( xy + x + y + 1 )

b) ( x + y )³ - ( x - y )³

C1. = x³ + 3x²y + 3xy² + y³ - ( x³ - 3x²y + 3xy² - y³ )

      = x³ + 3x²y + 3xy² + y³ - x³ + 3x²y - 3xy² + y³

      = 6x²y + 2y³

      = 2y( 3x² + y² )

C2. = [ ( x + y ) - ( x - y ) ][ ( x + y )² + ( x + y )( x - y ) + ( x - y )² ]

      = ( x + y - x + y )( x² + 2xy + y² + x² - y² + x² - 2xy + y² )

      = 2y( 3x² + y² )

c) 3x⁴y² + 3x³y² + 3xy² + 3y²

= 3( x⁴y² + x³y² + xy² + y² )

= 3[ ( x⁴y² + x³y² ) + ( xy² + y² ) ] 

= 3[ x³y²( x + 1 ) + y²( x + 1 ) ] 

= 3( x + 1 )( x³y² + y² )

= 3y²( x + 1 )( x³ + 1 )

= 3y²( x + 1 )( x + 1 )( x² - x + 1 )

= 3y²( x + 1 )²( x² - x + 1 )

d) 4( x² - y² ) - 8( x - ay ) - 4( a² - 1 )

= 4[ ( x² - y² ) - 2( x - ay ) - ( a² - 1 )

= 4( x² - y² - 2x + 2ay - a² + 1 )

= 4[ ( x² - 2x + 1 ) - ( y² - 2ay + a² ) ]

= 4[ ( x - 1 )² - ( y - a )² ]

= 4[ ( x - 1 ) - ( y - a ) ][ ( x - 1 ) + ( y + a ) ]

= 4( x - y + a - 1 )( x + y + a - 1 )

a) x² + 2x - 8 = x² - 2x + 4x - 8 = x(x - 2) + 4(x - 2) = (x - 2)(x - 4)

b) x² + 5x + 6 = x² + 2x + 3x + 6 = x(x + 2) + 3(x + 2) = (x + 2)(x + 3)

c) 4x² - 12x + 8 = 4x² - 4x - 8x + 8 = 4x(x - 1) - 8(x - 1) = (x - 1)(4x - 8)

d) 3x² + 8xy + 5y² = 3x² + 3xy + 5xy + 5y² = 3x(x + y) + 5y(x + y) = (x + y)(3x + 5y)

a) x² + 2x - 8 = x² - 2x + 4x - 8 = x( x - 2 ) + 4( x - 2 ) = ( x - 2 )( x + 4 )

b) x² + 5x + 6 = x² + 2x + 3x + 6 = x( x + 2 ) + 3( x + 2 ) = ( x + 2 )( x + 3 )

c) 4x² - 12x + 8 = 4( x² - 3x + 2 ) = 4( x² - x - 2x + 2 ) = 4[ x( x - 1 ) - 2( x - 1 ) ] = 4( x - 1 )( x - 2 )

d) 3x² + 8xy + 5y² = 3x² + 3xy + 5xy + 5y² = 3x( x + y ) + 5y( x + y ) = ( x + y )( 3x + 5y )