Question

Add:
(i) 3a − 2b + 5c, 2a + 5b − 7c, − a − b + c
(ii) 8a − 6ab + 5b, −6a − ab − 8b, −4a + 2ab + 3b
(iii) 2x³ − 3x² + 7x − 8, −5x³ + 2x² − 4x + 1, 3 − 6x + 5x² − x³
(iv) 2x² − 8xy + 7y² − 8xy², 2xy² + 6xy − y² + 3x², 4y² − xy − x² + xy²
(v) x³ + y³ − z³ + 3xyz, − x³ + y³ + z³ − 6xyz, x³ − y³ − z³ − 8xyz
(vi) 2 + x − x² + 6x³, −6 −2x + 4x² −3x³, 2 + x², 3 − x³ + 4x − 2x²

Answer 1

(i) Sum of the given expressions
= (3a − 2b + 5c)+(2a + 5b − 7c)+ (− a − b + c)
Rearranging and collecting the like terms
= 3a+2a-a-2b+5b-b+5c-7c+c
= (3+2-1)a + (-2+5-1)b + (5-7+1)c
= 4a+2b-c


(ii) Sum of the given expressions
= (8a − 6ab + 5b) + (−6a − ab − 8b) + (−4a + 2ab + 3b)
Rearranging and collecting the like terms
=(8−6−4)a + (- 6 −1+2)ab + (5− 8+ 3)b
= -2a-5ab+0 = -2a - 5ab

(iii) Sum of the given expressions
= (2x³ − 3x² + 7x − 8) + (−5x³ + 2x² − 4x + 1) + ( 3 − 6x + 5x² − x³ )
Rearranging and collecting the like terms
=2x³−5x³ − x³ − 3x² + 2x² + 5x² +7x-4x-6x-8+1+3
= (2-5-1)x³ +(-3+2+5)x²+(7-4-6)x-4
= -4x³ +4x²-3x-4


(iv) Sum of the given expressions
= (2x² − 8xy + 7y² − 8xy²)+( 2xy² + 6xy − y² + 3x²)+( 4y² − xy − x² + xy² )
Rearranging and collecting the like terms
= 2x² +3x² − x² + 7y² − y² +4y² − 8xy + 6xy − xy− 8xy² +2xy² + xy²
= (2 +3− 1)x² + (7 − 1 +4)y² + (-8 + 6 −1)xy + (− 8 +2 +1)xy²
= 4x² + 10y² − 3xy -5xy²

(v) Sum of the given expressions
= (x³ + y³ − z³ + 3xyz)+(− x³ + y³ + z³ − 6xyz)+(x³ − y³ − z³ − 8xyz)
Rearranging and collecting the like terms
= x³ -x³ + x³ + y³ + y³ − y³ -z³ + z³ − z³ + 3xyz-6xyz-8xyz
= (1-1+1)x³ + (1+1-1)y³ + (-1+1-1)z³ +(3-6-8)xyz
= x³ + y³ − z³ -11xyz

(vi) Sum of the given expressions
= (2 + x − x² + 6x³)+(−6 −2x + 4x² −3x³)+( 2 + x²)+( 3 − x³ + 4x − 2x² )
Rearranging and collecting the like terms
= 6x³ −3x³− x³− x² +4x²+ x²− 2x²+ x −2x+ 4x+2-6+2+3
= (6-3-1)x³+(-1+4+1-2)x²+(1-2+4)x+1
= 2x³+2x²+3x+1