Question

1, (x+3)(x+4)(x+5)(x+6)+1

2, x^2-2x(y+2)+y^2+4y+4

3, x^2+y^2+2x+2y+2(x+1)(y+1)+2

phân tích đa thức thành nhân tử

 

 

Answer 1

( x + 3 )( x + 4 )( x + 5 )( x + 6 ) + 1 

= [ ( x + 3 )( x + 6 ) ][ ( x + 4 )( x + 5 ) ] + 1

= ( x² + 9x + 18 )( x² + 9x + 20 ) + 1

= ( x² + 9x + 19 - 1 )( x² + 9x + 19 + 1 ) 1 

= ( x² + 9x + 19 )² - 1² + 1 = ( x² + 9x + 19 )²

Answer 2

x² - 2x( y + 2 ) + y² + 4y + 4

= x² - 2x( y + 2 ) + ( y + 2 )²

= ( x - y - 2 )²

Answer 3

x² + y² + 2x + 2y + 2( x + 1 )( y + 1 )

= ( x² + 2x + 1 ) + ( y² + 2y + 1 ) + 2( x + 1 )( y + 1 )

= ( x + y + 2 )²