Phân tích à ? -.-

a) ax - bx + ab - x²

= ( ax + ab ) - ( x² + bx )

= a( x + b ) - x( x + b )

= ( x + b )( a - x )

b) x² - 4xy + 4y² - 4

= ( x² - 4xy + 4y² ) - 4

= ( x - 2y )² - 2²

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

c) ( x² + y² - 2 )² - ( 2xy - 2 )²

= [ ( x² + y² - 2 ) - ( 2xy - 2 ) ][ ( x² + y² - 2 ) + ( 2xy - 2 ) ]

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

= ( x² - 2xy + y² )[ ( x² + 2xy + y² ) - 4 ]

= ( x - y )²[ ( x + y )² - 2² ]

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

d) ab( x² + y² ) + ( a² + b² ) ( cái này không phân tích được ((: )

a)\(69^2-31^2=\left(69-31\right)\left(69+31\right)=38.100=3800\)

\(1023^2-23^2=\left(1023-23\right)\left(1023+23\right)=1000.1046=1046000\)

Bài 1: 

a) Ta có: \(\left(15x^2\cdot y^2\cdot z\right):3xyz\)

\(=\dfrac{15x^2y^2z}{3xyz}\)

\(=5xy\)

b) Ta có: \(3x^2\cdot\left(5x^2-4x+3\right)\)

\(=3x^2\cdot5x^2-3x^2\cdot4x+3x^2\cdot3\)

\(=15x^4-12x^3+9x^2\)

c) Ta có: \(\left(2x^2-3x\right):\left(x-4\right)\)

\(=\dfrac{2x^2-8x+5x-20+20}{x-4}\)

\(=\dfrac{2x\left(x-4\right)+5\left(x-4\right)+20}{x-4}\)

\(=2x+5+\dfrac{20}{x-4}\)

d) Ta có: \(-5xy\cdot\left(3x^2y-5xy+y^2\right)\)

\(=-5xy\cdot3x^2y+5xy\cdot5xy-5xy\cdot y^2\)

\(=-15x^3y^2+25x^2y^2-5xy^3\)

Ta có:

$A=\frac{3^{10}.11+3^{10}.5}{3^9{.2}^4}=\frac{3^{10}.\left(11+5\right)}{3^9.16}$

$=\frac{3^{10}.16}{3^9.16}=\frac{3.1}{1.1}=3$

Vậy giá trị biểu thức A là 3

1 + 2xy - x² - y²

= 1 - ( x² - 2xy + y² )

= 1² - ( x - y )²

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

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

a² + b² - c² - d² - 2ab + 2cd

= ( a² - 2ab + b² ) - ( c² - 2cd + d² )

= ( a - b )² - ( c - d )²

= [ ( a - b ) - ( c - d ) ][ ( a - b ) + ( c - d ) ]

= ( a - b - c + d )( a - b + c - d )

a³b³ - 1

= ( ab )³ - 1³

= ( ab - 1 )[ ( ab )² + ab.1 + 1² ]

= ( ab - 1 )( a²b² + ab + 1 )

x²( y - z ) + y²( z - x ) + z²( x - y )

= z²( x - y ) + x²y - x²z + y²z + y²x

= z²( x - y ) + ( x²y - y²x ) - ( x²z - y²z )

= z²( x - y ) + xy( x - y ) - z( x² - y² )

= z²( x - y ) + xy( x - y ) - z( x + y )( x - y )

= ( x - y )[ z² + xy - z( x + y ) ]

= ( x - y )( z² + xy - zx - zy )

= ( x - y )[ ( z² - zx ) - ( zy - xy ) ]

= ( x - y )[ z( z - x ) - y( z - x ) ]

= ( x - y )( z - x )( z - y )

f