Question

Dados os polinômios: A = 2x - 3y + z B = x-y+2z C=3x+2y-3z D= x+y+5z
Calcule
A) A+B+C =
B) A-(B+C) - D =
C) A-B+C-D =
D) -[B-(C-A)] - D =

Answer 1

A ) A + B + C =

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

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

B ) A - ( B - C ) - D =

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

2x - 3y + z - x + y - 2z - 3x + 3z + 3x + 2y - 3z =

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

( 5x - 7x ) + ( - 5y + 2y ) + ( 4z - 5z ) = - 2x - 3y - z

C ) A - B + C - D =

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

2x - 3y + z - x + y - 2z + 3x + 2y - 3z - x - y - 5z =

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

( 5x - 2x ) + ( - 4y + 3y ) + ( z - 10z ) = 3x - y - 9z

D ) - [ B - ( C - A ) ] - D =

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

- [ x - y + 2z - 3x - 2y + 3z + 2x - 3y + z ] - x - y - 5z =

- x + y - 2z + 3x + 2y - 3z - 2x + 3y - z - x - y - 5z =

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

( - 4x + 3x ) + ( - y + 6y ) + ( - 11z ) = - x + 5y - 11z