Exercise 3.2 (Addition and Subtraction of Algebraic expressions)

Exercise 3.2

1. Fill in the blanks.

(i) The addition of −7b and 2b is –7b + 2b = –5b.

(ii) The subtraction of 5m from −3m is –3m – 5m = –8m

(iii) The additive inverse of − 37xyz is 37 xyz

2. Say True or False.

(i) The expressions 8x + 3y and 7x + 2y can not be added. (False)

(ii) If x is a natural number, then x + 1 is its predecessor. (False)

(iii) Sum of a − b + c and −a + b − c is zero. (True)

3. Add: (i) 8x, 3x, (ii) 7mn, 5mn (iii) −9y, 11y, 2y

(i) 8x, 3x

8x + 3x = 11 x

(ii) 7mn, 5mn

7mn + 5mn =12 mn

(iii) –9y, l l y, 2y

–9y + 11y + 2y

–9y + 13y = 4y

4. Subtract:

(i) 4k from 12k (ii) 15q from 25q (iii) 7xyz from 17xyz.

i) 4k from 12k = 12k – 4k = 8k

ii) 15q from 25q = 25q – 15q = 10q

iii) 7xyz from 17xyz = 17xyz – 7xyz = 10xyz

5. Find the sum of the following expressions

(i) 7p + 6q, 5p − q, q + 16p

(ii) a + 5b + 7c, 2a + 10b + 9c

(iii) mn + t, 2mn − 2t, − 3t + 3mn

(iv) u + v, u − v, 2u + 5v, 2u − 5v.

(v) 5xyz − 3xy, 3zxy − 5yx

(i) 7p + 6q, 5p – q, q + 16p

7p + 6q + 5p – q + q + 16p

7p + 5p + 16p + 6q – q + q

(7 + 5 + I6)p + (6 – 1 + l)q

28p + 6q

(ii) a + 5b + 7c, 2a + 106 + 9c

a + 5b + 7c + 2a + 10b + 9c

a4 – 2a + 5b + 10b + 7c + 9c

(1+2) a + (5 + 10) b + (7 + 9) c

3a + 15b + 16c

(iii) mn + t, 2mn – 2t, – 3t + 3mn

mn + t + 2mn – 2t – 3t + 3mn

mn + 2mn + 3mn + t – 2t – 3t

(1 + 2 + 3) mn + (1 – 2 – 3) t

6mn – 4t

(iv) u + v, u – v, 2u + 5v, 2u – 5v.

u + v + u – v + 2u + 5v + 2u – 5v

(1 + 1 + 2 + 2)u + (1 – 1 + 5 – 5)v

6u + Ov

6u

(v) 5xyz – 3xy, 3zxy – 5yx

5xyz – 3xy + 3zxy – 5yx

(5+3) xyz + (–3–5).xy

8 xyz – 8 xy 

6. Subtract

(i) 13x + 12y − 5 from 27x + 5y − 43

(ii) 3p + 5 from p − 2q + 7

(iii) m + n from 3m − 7n.

(iv) 2y + z from 6z − 5y.

(i) 13x + 12y – 5 from 27x + 5y – 43

27x + 5y– 43 – (13x + 12y – 5)

27x + 5y – 43 –13x –12y + 5

(27 –13) x + (5 – 12) y+ (–43 +5)

14x –7y – 38

(ii) 3p + 5 from p – 2q + 7

p – 2q + 7 – (3p + 5)

p – 2q + 7 – 3p – 5

(l–3) p + (–2q) + (7 – 5)

–2p – 2q + 2

(iii) m + n from 3m – 7n.

3m – 7n – (m + n)

3m – 7n – m – n

(3 – l)m + (–7 –1)n

2m – 8n

(iv) 2y + z from 6z – 5y.

6z – 5y – (2y + z)

6z – 5y – 2y – z

 (–5 –2) y + (6 – 1) z

–7y + 5z

7. Simplify

(i) (x + y − z) + (3x − 5y + 7z) − (14x + 7y − 6z)

(ii) p + p + 2 + p + 3 − p − 4 − p − 5 + p + 10

(iii) n + (m + 1) + (n + 2) + (m + 3) + (n + 4) + (m + 5)

(i) (x +y– z) + (3x – 5y+ 7z) – (14x + 7y– 6z)

x+y – z + 3x – 5y + 7z – 14x – 7y + 6z

x + 3x – 14x + y – 5y – 7y – z + 7z + 6z

(1 + 3 – 14) x + (1 – 5 – 7) y + (–1 +7 +6)z

–10x – 11y + 12z

(ii) p + p +2 + p + 3 – p – 4 – p – 5 + p + 10

p + p + p + p – p – p + 2 + 3 – 4 – 5 + 10

(1 + 1 + 1 + 1 – 1 – l)p + 2 + 3 + 10 – 4 – 5

(4 – 2)p + 15 – 9

2p + 6

(iii) n + (m + 1) + (n + 2) + (m + 3) + (n + 4) + (m + 5)

n + m + l + n + 2 + m + 3 + n + 4 + m + 5

m + m + m + n + n + n + 1 + 2 + 3 + 4 + 5

(1 + 1 + l)m + (1 + 1 + l)n + 15

3m + 3n + 15

Objective type questions

8. The addition of 3mn, −5mn, 8mn and −4mn is

(i) mn

(ii) −mn

(iii) 2mn

(iv) 3mn

Answer : (iii) 2mn

9. When we subtract ‘a’ from ‘– a’, we get _______

(i) 0

(ii) 2a

(iii) −2a

(iv) –a

Answer : (iii) –2a

10. In an expression, we can add or subtract only…

(i) Like terms

(ii) Unlike terms

(iii) All terms

(iv) None of the above

Answer : (i) Like terms

ANSWERS

EXERCISE-3.2

1. (i) –5b (ii) –8m (iii) 37xyz

2. (i) False (ii) False (iii) True

3. (i) 11x (ii) 12mn (iii) 4y

4. (i) 8k (ii) 10q (iii) 10xyz

5. (i) 28 p + 6q (ii) 3a + 15b + 16c (iii) 6 mn − 4t (iv) 6u (v) 8 xyz − 8xy

6. (i) 14x − 7y − 38 (ii) −2 p − 2q + 2 (iii) 2 m − 8n (iv) −7 + 5

7. (i) −10 x − 11y + 12z (ii) 2p + 6 (iii) 3m + 3n + 15

Objective type questions

8. (iii) 2mn

9. (iii) −2a

10. (i) Like terms