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Chapter 7: Algebraic Expressions Exercise – 7.3 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 Solution: 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. Solution: (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))
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
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)
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.
(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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Chapter 7: Algebraic Expressions Exercise –...