Addition and Subtraction of Algebraic Expressions – Maharashtra Board Class 6 Solutions for Mathematics

Addition and Subtraction of Algebraic Expressions – Maharashtra Board Class 6 Solutions for Mathematics (English Medium)

MathematicsGeneral ScienceMaharashtra Board Solutions

Exercise-54

Solution 1:

1. 12c + 7c
   = (12 + 7)c
   = 19c
2. bc² + 11bc²
   = (1 + 11)bc²
   = 12 bc²
3. -xyz + 2xyz
   = (-1 + 2)xyz
   = xyz
4. (-6a²b²) + (-46a²b²)
   = [(-6) + (-4)] a²b²
   = -10 a²b²
5. 10p²q + (- qp²)
   = (10 – 1) p²q
   = 9p²q
6. a³ + (-14a³)
   = (1 – 14) a³
   = -13a³

Solution 2:

Exercise-55

Solution 1:

1. 15x and 7y
   = 15x + 7y
   (Both are unlike terms so we cannot add their coefficients)
2. 23m²n and -9m²n
   = 23m²n – 9m²n
   (Both are unlike terms so we cannot add their coefficients)
3. 12a²b, 13 ab²
   =12a²b + 13 a²b
   (Both are unlike terms so we cannot add their coefficients)
4. 5a², 19b², c²
   = 5a²+ 19b² + c²
   (All are unlike terms so we cannot add their coefficients)
5. -6n, 4m, -2n
   = 4m + (-6n) + (-2n) (Writing the like terms together)
   = 4m -8n
6. 3ab, -4bc, 2bc
   = 3ab + (-4bc) + (2bc) (Writing the like terms together)
   = 3ab – 2bc
7. 18d, 10d², -8d, d²
   =18d + (-8d) + 10d² + d² (Writing the like terms together)
   = 10d + 11d²
   = 11d² + 10d
8. 11x², -21y², 9x², 11y²
   = 11x² + 9x² + (-21y²) + 11y² (Writing the like terms together)
   = 20x²– 10y²
9. a, 2b, 2c, -c, -b, 3a
   = a + 3b + 2b + (-b) + 2c + (-c) (Writing the like terms together)
   = 4a + b + c
10. 3a, 4a³, -5a²
    = 3a + 4a³ + (-5a²)
    (All are unlike terms so we cannot add their coefficients)
    = 4a³ – 5a² + 3a

Exercise-56

Solution 1:

1. 9p + 7q, 2p + 5q
   = (9p + 7q) + (2p + 5q)
   = (9p + 2p) + (7q + 5q)
   (Writing the like terms together)
   = 11p + 12q
2. 6m² + 7n², 11n² + 4m²
   = (6m² + 7n²) + (11n² + 4m²)
   = (6m²+ 4m²) + (7n² + 11n²)
   (Writing the like terms together)
   = 10m² + 18n²
3. 3a²– 2b², 5b² – a²
   = (3a² – 2b²) + (5b² – a²)
   = (3a² – a²) + (-2b² + 5b²)
   (Writing the like terms together)
   = 2a² + 3b²
4. 3b + 4c – d, 2d – c + 7b
   = (3b + 4c – d) + (2d – c + 7b)
   = (3b + 2d) + (4c – c) + (-d + 2d)
   (Writing the like terms together)
   = 5d + 3c + d
5. x + y + 2z, 2y + z + x
   = (x + y + 2z) + (2y + z + x)
   = (x + x) + (y + 2y) + (2z + z)
   (Writing the like terms together)
   = 2x + 3y + 3z
6. 2p + 3q + 4c, 4q – 5p
   = (2p + 3q + 4c) + (4q – 5p)
   = (2p – 5p) + (3q + 4q) + 4c
   (Writing the like terms together)
   = -3p + 7q + 4c

Solution 2:

Exercise-57

Solution 1(1):

Solution 1(2):

Solution 1(3):

Solution 1(4):

Solution 1(5):