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# Exercise 3.1 (Multiplication of Algebraic Expressions)

8th Maths : Chapter 3 : Algebra : Multiplication of Algebraic Expressions : Exercise 3.1 : Text Book Back Exercises Questions with Answers, Solution

Exercise 3.1

1. Complete the table.

Solution:

2. Find the product of the terms.

(i) 2mn , (2m)2 , 3mn (ii) 3x 2 y , 3xy3 , x 2 y2

Solution:

(i) (−2mn) × (2m)2 × (−3mn) = (−2mn) × 22m2 × (−3mn) = (− 2mn) × 4m2 × (− 3mn)

= (−) (+) (−) (2 × 4 × 3) (m × m2 × m) (n × n)

= + 24 m4 n2

(ii) (3x2y) × (−3xy3) × (x2y2) = (+) × (−) × (+) × (3 × 3 × 1) (x2 × x × x2) × (y × y3 × y2 )

= −9x5y6

3. If l = 4 pq2 , b = −3p2q , h = 2 p3 q3 then, find the value of l × b × h .

Solution:

Given l = 4pq2

b = −3p2q

h = 2p3q3

l × b × h = (4pq2) × (−3p2q ) × (2p3q3)

= (+) (−) (+) (4 × 3 × 2) (p × p2 × p3) (q2 × q × q3)

= −24p6q6

4. Expand

(i) 5x (2 y 3)

(ii) 2 p(5p2 3p + 7)

(iii) 3mn(m3n3 5m2n + 7mn2

(iv) x2 (x + y + z) + y2 (x + y + z) + z2 (x y z)

(i) 5x (2y − 3)

5x (2y − 3) = (5x)(2y) − (5x)(3)

= (5 × 2)(x × y) − (5 × 3)x

= 10xy − 15x

(ii) −2p (5p2 −3p + 7)

−2p (5p2 −3p + 7) = (−2p) (5p2) + (−2p) (−3p) + (−2p) (7)

= [(−) (+) (2 × 5) (p × p2)] + [(−) (−) (2 × 3) (p × p)] + (−)(+)(2 × 7) p

= −10p3 + 6p2 − 14p

(iii) 3mn(m3n3 – 5m2n + 7 mn2)

3mn(m3n3 – 5m2 n + 7 mn2) = (3mn) (m3n3) + (3mn) (−5m2n) + (3mn)(7mn2)

= (3) (m × m3) (n × n3) + (+) (−) (3 × 5) (m × m2) (n × n) + (3 × 7) (m × m)(n × n2)

= 3m4 n4 − 15m3 n2 + 21m2n3

(iv) x2(x + y + z) + y2(x + y + z) + z2(xyz)

x2 (x + y + z) + y2 (x + y + z) + z2(xyz) = (x2 × x) + (x2 × y) + (x2 × z ) + (y2 × x) + (y2 × y) + (y2 × z) + (z2 × x) + z2 (−y) + z2 (−z)

= x3 + x2y + x2z + xy2 + y3 + y2z + xz2yz2z3

= x3 + y3z3 + x2y + x2z + xy2 + zy2 + xz2yz2

5. Find the product of

(i) (2x + 3)(2x − 4)

(ii) ( y2 − 4)(2 y2 + 3y)

(iii) (m2n)(5m2n2 − n2 )

(iv) 3(x − 5) × 2(x −1)

Solution:

(i) (2x + 3) (2x − 4)

(2x + 3) (2x − 4) = (2x) (2x − 4) + 3(2x − 4)

= (2x × 2x) − 4(2x) + 3(2x) − 3(4)

= 4x2 − 8x + 6x − 12 = 4x2 + (− 8 + 6)x − 12

= 4x2 − 2x – 12

(ii) (y2 − 4) (2y2 + 3y)

(y2 − 4) (2y2 + 3y) = y2(2y2 + 3y) – 4 (2y2 + 37)

= y2 (2y2) + y2(3y) − 4(2y2) − 4(3y)

= 2y4 + 3y3 − 8y2 12y

(iii) (m2 n) (5m2n2n2)

(m2 n) (5m2n2 n2) = m2 (5m2n2n2) − n (5m2n2n2)

= m2 (5m2n2) + m2(−n2) − n(5m2n2) + (−)(−)n(n2)

= 5m2n2 m2n2 5m2n3 + n3

(iv) 3(x − 5) × 2(x − 1)

3(x − 5) × 2(x − 1) = (3 × 2) (x − 5) (x − 1)

= 6 × [x (x − 1) − 5 (x − 1)]

= 6 [x.xx . 1 − 5x + (−1) (−) 5 1 ]

= 6 [x2x − 5x + 5] = 6 [x2 + (−1 −5)x + 5]

= 6 [x2 − 6x + 5] = 6x2 − 36x + 30

6. Find the missing term

(i) 6xy × _________ = −12x3

(ii) _________× ( −15m2n3p) = 45m3n3p2

(iii) 2y (5x2 y − ___+ 3 ___) = 10x2y2 − 2xy + 6y3

Solution:

(i) 6xy × = (−2x2 ) = −12x3y

(ii) −3mp  × (−15m2n3p) = 45m3n3p2

(iii) 2y(5x2yx + 3y2) = 10x2y2 − 2xy + 6y3

7. Match the following.

a) 4y2 × −3y (i) 20x2 y − 20x

b) −2xy(5x2 − 3) (ii) 5x3 − 5xy2 + 5x2y

c) 5x (x2 y2 + xy) (iii) 4x2 − 9

d) (2x + 3)(2x − 3) (iv) −12 y3

e) 5x (4xy − 4) (v) −10x3y + 6xy

A) iv, v, ii, i, iii

B) v, iv, iii, ii, i

C) iv, v, ii, iii, i

D) iv, v, iii, ii, i

[Answer C : (a)−iv, (b)−v, (c)−ii, (d)−iii, (e)−i]

8. A car moves at a uniform speed of ( x + 30) km/hr. Find the distance covered by the car in ( y + 2) hours. (Hint: distance = speed × time).

Solution:

Sppeed of the car = (x + 30) km / hr.

Time = (y + 2) hours

Distance = Speed × time

= (x + 30) (y + 2) = x(y + 2) + 30(y + 2)

= (x) (y) + (x) (2) + (30) (y) + (30) (2)

= xy + 2x + 30y + 60

Distance covered = (xy + 2x + 30y + 60) km

Objective Type Questions

9. The product of 7 p3 and (2 p2)2 is

(A) 14 p12

(B) 28 p7

(C) 9 p7

(D) 11p12

10. The missing terms in the product −3m3n × 9(__) = _________ m4n3 are

(A) mn2 , 27

(B) m2n, 27

(C) m2n2 , 27

(D) mn2 , 27

11. If the area of a square is 36x4 y2 then, its side is ____________

(A) 6x 4 y2

(B) 8x 2 y2

(C) 6x 2 y

(D) 6x 2 y

12. If the area of a rectangle is 48m2n3 and whose length is 8mn2 then, its breadth is__.

(A) 6 mn

(B) 8m2n

(C) 7m2n2

(D) 6m2n2

13. If the area of a rectangular land is (a 2 b2 ) sq.units whose breadth is (a b) then, its length is__________

(A) a b

(B) a + b

(C) a 2 b

(D) (a + b)2

Exercise 3.1

1.

2. (i) 24m4 n2  (ii) 9x5 y6

3. − 24 p 6 q6

4. (i) 10 xy 15x (ii) − 10 p 3 + 6 p214 p

(iii ) 3m4 n 4 15m3 n 2 + 21m2 n3

(iv) x3 + y3 z3 + x2y + x2z + xy2 + zy2 + xz2 yz2

5. (i ) 4x2 2 x 12

(ii) 2 y 4 + 3y3 8 y 2 12 y

(iii) 5m4 n2 - m2 n 2 - 5m2 n 3 + n3

(iv) 6x2 - 36 x + 30

6. (i) − 2x2 ii) 3mp iii) y(5x 2 y x + 3y2 )

7. (C) iv, v, ii, iii, i

8. xy + 2x + 30 y + 60

9. (B) 28p7

10. (D) mn2, –27

11. (C) 6x2 y

12. (A) 6 mn

13. (B) (a+b)

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