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

MathematicsGeneral ScienceMaharashtra Board Solutions

### Exercise-54

**Solution 1:**

- 12c + 7c

= (12 + 7)c

= 19c - bc
^{2}+ 11bc^{2}

= (1 + 11)bc^{2}

= 12 bc^{2} - -xyz + 2xyz

= (-1 + 2)xyz

= xyz - (-6a
^{2}b^{2}) + (-46a^{2}b^{2})

= [(-6) + (-4)] a^{2}b^{2}

= -10 a^{2}b^{2} - 10p
^{2}q + (- qp^{2})

= (10 – 1) p^{2}q

= 9p^{2}q - a
^{3}+ (-14a^{3})

= (1 – 14) a^{3}

= -13a^{3}

**Solution 2:**

### Exercise-55

**Solution 1:**

- 15x and 7y

= 15x + 7y

(Both are unlike terms so we cannot add their coefficients) - 23m
^{2}n and -9m^{2}n

= 23m^{2}n – 9m^{2}n

(Both are unlike terms so we cannot add their coefficients) - 12a
^{2}b, 13 ab^{2}

=12a^{2}b + 13 a^{2}b

(Both are unlike terms so we cannot add their coefficients) - 5a
^{2}, 19b^{2}, c^{2}

= 5a^{2}+ 19b^{2}+ c^{2}

(All are unlike terms so we cannot add their coefficients) - -6n, 4m, -2n

= 4m + (-6n) + (-2n) (Writing the like terms together)

= 4m -8n - 3ab, -4bc, 2bc

= 3ab + (-4bc) + (2bc) (Writing the like terms together)

= 3ab – 2bc - 18d, 10d
^{2}, -8d, d^{2}

=18d + (-8d) + 10d^{2}+ d^{2}(Writing the like terms together)

= 10d + 11d^{2}

= 11d^{2}+ 10d - 11x
^{2}, -21y^{2}, 9x^{2}, 11y^{2}

= 11x^{2}+ 9x^{2}+ (-21y^{2}) + 11y^{2}(Writing the like terms together)

= 20x^{2}– 10y^{2} - a, 2b, 2c, -c, -b, 3a

= a + 3b + 2b + (-b) + 2c + (-c) (Writing the like terms together)

= 4a + b + c - 3a, 4a
^{3}, -5a^{2}

= 3a + 4a^{3}+ (-5a^{2})

(All are unlike terms so we cannot add their coefficients)

= 4a^{3}– 5a^{2}+ 3a

### Exercise-56

**Solution 1:**

- 9p + 7q, 2p + 5q

= (9p + 7q) + (2p + 5q)

= (9p + 2p) + (7q + 5q)

(Writing the like terms together)

= 11p + 12q - 6m
^{2}+ 7n^{2}, 11n^{2}+ 4m^{2}

= (6m^{2}+ 7n^{2}) + (11n^{2}+ 4m^{2})

= (6m^{2}+ 4m^{2}) + (7n^{2}+ 11n^{2})

(Writing the like terms together)

= 10m^{2}+ 18n^{2} - 3a
^{2}– 2b^{2}, 5b^{2}– a^{2}

= (3a^{2}– 2b^{2}) + (5b^{2}– a^{2})

= (3a^{2}– a^{2}) + (-2b^{2}+ 5b^{2})

(Writing the like terms together)

= 2a^{2}+ 3b^{2} - 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 - 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 - 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):**