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) 2a^{2} − b^{2} − 3ab + 6
(vi) a^{2} + b^{2}^{ }− c^{2} + ab − 3ac
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) 2a^{2} − b^{2} − 3ab + 6 = 2a^{2} − b^{2} − (3ab  6)
(vi) a^{2}^{ }+ b^{2} − c^{2} + ab − 3ac = a^{2}^{ }+ b^{2} − c^{2}  ( ab + 3ac)
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 x^{2} − y^{2} + 4xy from 2x^{2} + y^{2} − 3xy is added to 9x^{2} − 3y^{2} − xy.
(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 x^{2} − y^{2} + 4xy from 2x^{2} + y^{2} − 3xy is given by {(2x^{2} + y^{2} − 3xy)  (x^{2} − y^{2} + 4xy)}.
When the above equation is added to 9x^{2} − 3y^{2} − xy, we get
{(2x^{2} + y^{2} − 3xy)  (x^{2} − y^{2} + 4xy)} + (9x^{2} − 3y^{2} − xy)
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