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# Exercise 3.2 (Division of Algebraic Expressions)

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) [ 18m4 (n8) ] / [ 2m(3)n3 ] = 9 mn5 ]

(ii) [l4m5n(7)] / [2lm(3)n6] = [l3m2n] / 2 ]

(iii) [ 42a4b5 (c2) ] / [ 6(a)4(b)2 ] = (7) b3 c2 ]

2. Say True or False

(i) 8x 3 y ÷ 4x2 = 2xy [Answer: True]

(ii) 7ab 3 ÷ 14ab = 2b2 [Answer: False]

3. Divide

(i) 27 y3 by 3y

(ii) x3 y2 by x2y

(iii) 45x3 y2z4 by (15xyz)

(iv) (3xy)2 by 9xy

Solution: (i) 27y3 / 3y = (27/3) y3−1 = 9y2

(ii) x3y2 / x2y = x3−2 y2−1 = x1y1 = xy

(iii) [ 45x3 y2z4  ] / [−15xyz] = (45/−15) x3−1 y2−1 y4−1z4−1 = −3x2 yz3

(iv) (3xy)2 / [ 3 × (3xy) ] = [ (3xy)2 ] / [3 × (3xy)] = (1/3) (3xy)2−1 = (1/3) 3xy = xy

4. Simplify Solution: (i) [3m2 / m ] + [2 m4 / m3 ] = 3m2−1 + 2 m4−3 = 3m + 2m = (3 + 2) m = 5m

(ii) [ 14p5q3 / 2p2q ] – [ 12p3q4 / 3q2 ] = [ (14/2) p5−2q3−1 ] – [ 12/3 p3q4−3 ] = 7p3q2 − 4p3q2 = 3p2q2

5. Divide

(i) (32 y2 − 8 yz) by 2y

(ii) (4m2n3 + 16m4 n2 mn) by 2mn

(iii) 5xy2 - 18x2 y3 + 6xy by 6xy

(iv) 81( p4 q2r3 + 2 p3q3 r2 5p2 q2r2 ) by ( 3pqr)2

Solution: (i) (32y2 – 8yz) by 2y

[ 32y2 – 8yz ] / 2y = [32y2 / 2y ] – [ 8yz / 2y ] = (32/2) y2−1 – (8/2) y1−1z = 16y – 4z

(ii) (4m2 n3 + 16 m4 n2mn) by 2 mn

[ 4m2n3 + 16m4n2mn ] / 2mn = [4m2n3 / 2mn ] + [ 16m4n2 / 2mn ] – [ mn / 2mn]

= (4/2)m2−1 n3−1  + (16/2)m4−1 n2−1 – (1/2)m1−1n1−1

= 2m1n2  + 8 m3n1 – (1/2)m0n0

= 2mn2  + 8m3n – 1/2

(iii) 5xy2 − 18x2y3 + 6xy by 6xy

[ 5xy2 − 18x2y3 + 6xy ] / 6xy = [ xy(5y − 18xy2 + 6) ] / 6xy

= [ 5y − 18xy2 + 6 ] / 6 = (5/6) y − 3xy2 + 1

(iv) 81 (p4q2r3 + 2p3q3r2 − 5p2q2r2) by (3pqr)2

[ 81 (p4q2r3 + 2p3q3r2 − 5p2q2r2) ] / (3pqr)2

= [ 81 (p2q2r2) (p2r + 2pq− 5) ] / [ 9(p2q2r2) ]

= 81/9 (p2q2r2)1−1 (p2r + 2pq− 5)

= 9(p2r + 2pq− 5) = 9p2r + 18pq − 45

6. Identify the errors and correct them

(i) 7 y 2 y2 +3y 2 = 10 y2

(ii) 6xy + 3xy = 9x 2 y2

(iii) m(4m 3) = 4m23

(iv) (4n)22n + 3 = 4n 22n + 3

(v) (x 2)(x + 3) = x2 6

(vi) -3p2 + 4p - 7 = - (3p2 + 4p - 7)

Solution:

(i) 7y2 − y2 + 3y2 =  (7 – 1 + 3) y2  = (6 + 3) y2 = 9y2

(ii) 6xy + 3xy =  (6 + 3) xy = 9xy

(iii) m (4m − 3) = m (4m) + m (−3) = 4m2 − 3m

(iv) (4n)2 − 2n + 3 = 16n2 − 2n + 3

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

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

= x2 + 3x − 2x − 6 = x2 + x − 6

(vi) − 3p2 + 4p − 7 = − (3p2 − 4p +7)

7. Statement A: If 24p2q is divided by 3pq, then the quotient is 8p.

Statement B: Simplification of (5 x + 5) / 5 is 5x

(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: [24p2q] / [3pq] = 8p2 / p = 8p2−1 = 8p

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

8. Statement A: 4x 2 + 3x -2 = 2(2x2 + 3x/2 -1)

Statement B: (2m–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:

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

(2m − 5) + (2m − 5) = 4m − 10

Exercise 3.2

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

3. (i ) 9 y2 (ii) xy (iii ) − 3x2yz3 (iv) x y

4. (i) 5m (ii) 3p3q2

5. (i ) 16 y − 4z (ii) 2 mn2 + 8m3 n – 1/2 (iii ) (5/6)y - 3 xy2 + 1 (iv) = 9 p2r +18pq – 45

6. (i ) 9 y2 (ii) 9 xy (iii ) 4 m2 −3m (iv) 16 n2 − 2n + 3 (v) x2 + 1x − 6 (vi) –(3p2 –4p + 7)

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

8. (i) both A and B are true

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