RD Sharma solution class 7 chapter 7 Algebraic Expression Exercise 7.3

Exercise 7.3

Page-7.16

Question 1:

Place the last two terms of the following expressions in parentheses preceded by a minus sign:
(i) x + y − 3z + y
(ii) 3x − 2y − 5z − 4
(iii) 3a − 2b + 4c − 5
(iv) 7a + 3b + 2c + 4
(v) 2a² − b² − 3ab + 6
(vi) a² + b² − c² + ab − 3ac

Answer 1:

We have
(i) x + y − 3z + y = x  + y − (3z - y )
(ii) 3x − 2y − 5z − 4 = 3x - 2y - (5z + 4)
(iii) 3a − 2b + 4c − 5 = 3a - 2b - (- 4c + 5)
(iv) 7a + 3b + 2c + 4 = 7a + 3b - (- 2c - 4)
(v) 2a² − b² − 3ab + 6 = 2a² − b² − (3ab - 6)
(vi) a² + b² − c² + ab − 3ac = a² + b² − c² - (- ab + 3ac)

Question 2:

Write each of the following statements by using appropriate grouping symbols:
(i) The sum of a − b and 3a − 2b + 5 is subtracted from 4a + 2b − 7.
(ii) Three times the sum of 2x + y − {5 − (x − 3y)} and 7x − 4y + 3 is subtracted from 3x − 4y + 7.
(iii) The subtraction of x² − y² + 4xy from 2x² + y² − 3xy is added to 9x² − 3y² − xy.

Answer 2:

(i) The sum of a − b and 3a − 2b + 5 = {(a - b) + (3a − 2b + 5)}.
     This is subtracted from 4a + 2b - 7.
     Thus, the required expression is {4a + 2b - 7) - {(a - b) + (3a − 2b + 5)}.

(ii) Three times the sum of 2x + y − {5 − (x − 3y)} and 7x − 4y + 3 = 3[(2x + y) − {5 − (x − 3y)} + (7x − 4y + 3)].
      This is subtracted from 3x - 4y +7.
      Thus, the required expression is (3x - 4y +7) - 3[(2x + y) − {5 − (x − 3y)} + (7x − 4y + 3)].

(iii) The product of subtraction of x² − y² + 4xy from 2x² + y² − 3xy is given by {(2x² + y² − 3xy) - (x² − y² + 4xy)}.
       When the above equation is added to 9x² − 3y² − xy, we get
       {(2x² + y² − 3xy) - (x² − y² + 4xy)} + (9x² − 3y² − xy)

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