Question

Áp dụng HĐT thực hiện các phép tính sau:

a) (a - b -c)² - (a - b + c)²

b) (a - x - y)³ - (a + x - y)³

 

Answer 1

a) ( a - b - c )² - ( a - b + c )²

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

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

= -2c( 2a - 2b )

= -2c.2( a - b )

= -4c( a - b )

b) ( a - x - y )³ - ( a + x - y )³

= [ ( a - x - y ) - ( a + x - y ) ][ ( a - x - y )² + ( a - x - y )( a + x - y ) + ( a + x - y )² ]

= ( a - x - y - a - x + y ){ [ ( a - x ) - y ]² + [ ( a - y ) - x ][ ( a - y ) + x ] + [ ( a + x ) - y ] ² }

= -2x{ [ ( a - x )² - 2( a - x )y + y² ] + [ ( a - y )² - x² ] + [ ( a + x )² - 2( a + x )y + y² ] }

= -2x{ [ a² + x² + y² - 2ax - 2ay + 2xy ] + [ a² - x² + y² - 2ay ] + [ a² + x² + y² + 2ax - 2ay - 2xy ] }

= -2x{ a² + x² + y² - 2ax - 2ay + 2xy + a² - x² + y² - 2ay + a² + x² + y² + 2ax - 2ay - 2xy }

= -2x{ 3a² + x² + 3y² - 6ay } < trời ơi dài > ;-;