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))