Question

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 1

(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)