8th Maths : Chapter 3 : Algebra : Division of Algebraic Expressions: Exercise 3.2 : Text Book Back Exercises Questions with Answers, Solution

**Exercise 3.2**

** **

**1. Fill in the blanks:**

**(i) [ **18*m*^{4}
(**n^{8}**) ] / [ 2

**(ii) **[*l*^{4}*m*^{5}*n*^{(7)}]
/ [2*lm*^{(3)}*n*^{6}] = [*l*^{3}*m*^{2}*n*]
/ __2__ ]

**(iii) **[ 42*a*^{4}*b*^{5}
(**c^{2}**) ] / [ 6(

**2. Say True or False **

(i) 8*x* ^{3} *y* ÷ 4*x*^{2} =
2*xy*

(ii) 7*ab* ^{3} ÷
14*ab* = 2*b*^{2} **[Answer: False]**

**3. Divide **

**(i) 27 y^{3} by 3y **

**(ii) x^{3} y^{2}
by x^{2}y**

**(iii) 45 x^{3} y^{2}z^{4 }by (**

**(iv) (3 xy)^{2 }by 9xy**

**Solution:**

**(i) ****27 y^{3 }/ 3y **= (27/3)

**(ii) ***x*^{3}*y*^{2 }**/ x^{2}y **=

**(iii) [ ****45 x^{3} y^{2}z^{4 }] **/

**(iv) ****(3 xy)^{2} / [ 3 × (3xy) ]** = [ (3

** **

**4. Simplify**

**Solution:**

**(i) [3 m^{2}
/ m ] + [2 m^{4} / m^{3} ]** = 3

**(ii) [ 14 p^{5}q^{3}
/ 2p^{2}q ] – [ 12p^{3}q^{4}
/ 3q^{2} ]** = [ (14/2)

** **

**5. Divide **

**(i) (32 y^{2} − 8 yz) by
2y **

**(ii) (4 m^{2}n^{3}
**

**(iii) 5 xy^{2} - 18x^{2}
y^{3} + 6xy by 6xy **

**(iv) 81( p^{4} q^{2}r^{3} **

**Solution:**

**(i) (32 y^{2} – 8yz) by 2y**

**[ **32*y*^{2} – 8*yz* ]
/ 2*y*** = [**32*y*^{2} / 2*y *]* *– [ 8*yz* / 2*y* ]
= (32/2) *y*^{2−1}* *– (8/2)* y*^{1−1}*z* =
16*y *– 4*z*

**(ii) (4 m^{2} n^{3} + 16 m^{4}
n^{2} − mn) by 2 mn**

[ 4*m*^{2}*n*^{3} + 16*m*^{4}*n*^{2}
– *mn* ] / 2*mn* = [4*m*^{2}*n*^{3} / 2*mn*
] + [ 16*m*^{4}*n*^{2} / 2*mn* ] – [ *mn* /
2*mn*]

= (4/2)*m*^{2−1} *n*^{3−1} + (16/2)*m*^{4−1} *n*^{2−1}
– (1/2)*m*^{1−1}*n*^{1−1}

= 2*m*^{1}*n*^{2} + 8* m*^{3}*n*^{1}
– (1/2)*m*^{0}*n*^{0}

= 2*mn*^{2}
+ 8*m*^{3}*n*^{ }– 1/2

**(iii) 5 xy^{2} − 18x^{2}y^{3}
+ 6xy by 6xy**

[ 5*xy*^{2} − 18*x*^{2}*y*^{3}
+ 6*xy* ] / 6*xy*** = [ ***xy*(5*y* − 18*xy*^{2}
+ 6) ] / 6*xy*

**= [ **5*y* − 18*xy*^{2}
+ 6 ] / 6 = (5/6) *y* − 3*xy*^{2} + 1

**(iv) 81 ( p^{4}q^{2}r^{3}
+ 2p^{3}q^{3}r^{2} − 5p^{2}q^{2}r^{2})
by (3pqr)^{2}**

[ 81 (*p*^{4}*q*^{2}*r*^{3}
+ 2*p*^{3}*q*^{3}*r*^{2} − 5*p*^{2}*q*^{2}*r*^{2})
] / (3*pqr*)^{2}

= [ 81 (*p*^{2}*q*^{2}*r*^{2})
(*p*^{2}*r* + 2*pq*− 5) ] / [ 9(*p*^{2}*q*^{2}*r*^{2})
]

= 81/9 (*p*^{2}*q*^{2}*r*^{2})^{1−1}
(*p*^{2}*r* + 2*pq*− 5)

= 9(*p*^{2}*r* + 2*pq*− 5) = 9*p*^{2}*r*
+ 18*pq − *45

** **

**6. Identify the errors and correct them**

**(i) 7 y ^{2} **

**(ii) 6 xy **

**(iii) m(4m **

**(iv) (4 n)^{2}**

**(v) ( x **

**(vi) -3 p^{2} + 4p - 7 =
- (3p^{2} + 4p - 7)**

**Solution:**

**(i) **7*y*^{2 − }*y*^{2
}+ 3*y*^{2 }= (7 – 1 +
3) *y*^{2 } = (6 + 3)* y*^{2}
= 9*y*^{2}

**(ii)** 6*xy* + 3*xy *= (6 + 3) *xy* = 9*xy*

**(iii)** *m* (4*m* − 3) = *m*
(4*m*) + *m* (−3) = 4*m*^{2} − 3*m*

**(iv)** (4*n*)^{2} − 2*n*
+ 3 = 16*n*^{2} − 2*n* + 3

**(v)** (*x* − 2) (*x* + 3) = *x*
(*x* + 3) − 2 (*x* + 3)

= *x*(*x*) + (*x*)
× 3 + (−2) (*x*) + (−2) (3)

= *x*^{2} +
3*x* − 2*x* − 6 = *x*^{2} + *x* − 6

**(vi)** − 3*p*^{2} + 4*p*
− 7 = − (3*p*^{2} − 4*p* +7)

**7. Statement A: If 24 p^{2}q is divided by 3pq, then
the quotient is 8p.**

**Statement B: Simplification of (5 x **

(i) Both
A and B are true

(ii) A is
true but B is false

(iii) A is
false but B is true

(iv) Both
A and B are false

**[Answer: (ii) A is true but B is false]**

**Solution:**

[24*p*^{2}*q*] / [3*pq*]
= 8*p*^{2} / *p* = 8*p*^{2−1} = 8*p*

( [5*x* + 5] / 5 ) = [ 5(*x* + 1) ] / 5 = *x* + 1

**8. Statement A: 4 x ^{2} + 3x -2 = 2(2x^{2} +
3x/2 -1)**

**Statement B: (2 m–5)–(5–2m) = (2m–5) + (2m–5)**

(i) Both
A and B are true

(ii) A is
true but B is false

(iii) A is
false but B is true

(iv) Both
A and B are false

**[Answer: (i) Both A and B are true]**

**Solution:**

(2*m* − 5) − (5 − 2*m*) = 2*m* − 5 − 5 + 2*m*
= 4*m* − 10

(2*m* − 5) + (2*m* − 5) = 4*m − *10

** **

**Answer:**

**Exercise 3.2**

**1. **

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

**3. (i ) 9 y^{2} (ii) xy (iii ) − 3x^{2}yz^{3} (iv) x y**

**4. (i) 5 m (ii) 3p^{3}q^{2}
**

**5. (i ) 16 y − 4z (ii) 2 mn^{2} +
8m^{3} n – 1/2 (iii ) (5/6)y - 3 xy^{2} + 1 (iv) = 9 p^{2}r +18pq – 45**

**6. (i ) 9 y^{2} (ii) 9 xy (iii ) 4 m^{2}
−3m (iv) 16 n^{2} − 2n + 3 (v) x^{2} + 1x − 6 (vi) –(3p^{2}
–4p + 7)**

**7. (ii) A is true but B
is false **

**8. (i) both A and B are
true**

** **

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8th Maths : Chapter 3 : Algebra : Exercise 3.2 (Division of Algebraic Expressions) | Questions with Answers, Solution | Algebra | Chapter 3 | 8th Maths

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