RD Sharma Solutions Class 8 Factorization Exercise 7.2

RD Sharma Solutions Class 8 Chapter 7 Exercise 7.2

RD Sharma Class 8 Solutions Chapter 7 Ex 7.2 PDF Free Download

Factorize the following :

Q.1)  3x – 9 

Soln.:

The greatest common factor of the terms 3x and -9 of the expression 3x – 9 is 3.

Now,

3x = 3x

and

-9 = 3(-3)

Hence, the expression 3x – 9 can be factorised as 3(x – 3).

 

 

Q.2)  5x – 15x2

Soln.:

The greatest common factor of the terms 5x and 15x2 of the expression 5x – 15x2 is 5x.

Now,

5x = 5x.(1)

and

-15x2 = 5x.(-3x)

Hence, the expression 5x – 15x2 can be factorised as 5x(1 – 3x)

Q.3)  20a12b2  – 15a8b4       

Soln.:

The greatest common factor of the terms

20a12b2 and -15a8b4 of the expression 20a12b2 – 15a8b4 is 5a8b2.

20a12b2 = 5x4xa8xa4xb2 = 5a8xb2x4a4 and  -15a8xb4 = 5x(-3)xa8xb2xb2 = 5a8b2 x(-3)b2

Hence, the expression 20a12b2 – 15a8b4 can be factorised as 5a8b2(4a4 – 3b2)

Q.4)   72x6y7 – 96x7y6

Soln.:

The greatest common factor of the terms 72x6y7 and  -96x7y6 of the expression  72x6y7 – 96x7y64 is 24x6y6

Now,

72x6y7 =  24x6y6 . 3y

And,  – 96x7y64 is 24x6y6 . – 4x

Hence, the expression 72x6y7 –  96x7y6 can be factorised as 24x6y6 . (3y – 4x).

 

 

Q.5)   20x3 – 40x2 + 80x

Soln.:

The greatest common factor of the terms 20x3, -40x2 and 80x of the expression 20x3 – 40x2 +80x is 20x.

Now, 20x3 = 20x . x2

-40x2 = 20x . -2x

And,  80x = 20x . 4

Hence, the expression 20x3 – 40x2 +80x can be factorised as 20x(x2 – 2x + 4)

Q.6)   2x3y2 – 4x2y3 + 8xy4

Soln.:

The greatest common factor of the terms 2x3y2,  -4x2y3 and 8xy4 of the expression

2x3y– 4x2y3 + 8xy4 is 2xy2.

Now,

2x3y2 = 2xy2 . x2

-4x2y3 = 2xy2 . (-2xy)

8xy4 = 2xy2 . 4y2

Hence, the expression  2x3y– 4x2y3 + 8xy4 can be factorised as 2xy2(x2 – 2xy + 4y2)

Q.7)  10m3n2 + 15m4n – 20m2n3

Soln.:

The greatest common factor of the terms 103n2, 15m4n and -20m2n3 of the expression

10m3n2 + 15m4n – 20m2n3 is 5m2n.

Now,

10m3n2 = 5m2n . 2mn

15m4n = 5m2n . 3m2

-20m2n3 = 5m2n . -4n2

Hence, 10m3n2 + 15m2n – 20m2n3 can be factorised as 5m2n(2mn + 3m2 – 4n2)

 

 

Q.8)  2a4b4 – 3a3b5 + 4a2b5

Soln.:

The greatest common factor of the terms 2a4b4, -3a3b5 and 4a2b5 of the expression

2a4b4 – 3a3b5 + 4a2b5 is a2b5.

Now,

2a4b4 = a2b5 . 2a2

-3a3b5 = a2b4 . (-3ab)

4a2b5 = a2b4  . 4b

Hence,   2a4b4 – 3a3b5 + 4a2b5 can be factorised as a2b4(2a2 – 3ab + 4b)

Q.9)  28a2 + 14a2b2 – 21a4

Soln.:

The greatest common factor of the terms28a2, 14a2b2 and 21a4 of the expression

28a2 + 14a2b2 – 21a4 is 7a2.

Also, we can write 28a2 = 7a2. 4, 14a2b2 = 7a2 . 2b2 and 21a4 = 7a2 . 3a2.

Therefore, 28a2 + 14a2b2 – 21a4 = 7a2. 4  +  7a2 . 2b2 – 7a2 . 3a2

= 7a2 (4 + 2b2 – 3a2)

Q.10)  a4b – 3a2b2 – 6ab3

Soln.:

The greatest common factor of the terms a4b, 3a2b2 and 6ab3 of the expression

a4b – 3a2b2 – 6ab3 is ab.

Also, we can write a4b = ab . a3, 3a2b2 = ab . 3ab  and 6ab3 = ab . 6b2.

Therefore,   a4b – 3a2b2 – 6ab3 = ab . a3 – ab . 3ab – ab . 6b2.

= ab (a3 – 3ab – 6b2)

Q.11)  2L2mn – 3Lm2n + 4Lmn2

Soln.:  

The greatest common factor of the terms 2L2mn, 3Lm2n and 4Lmn2 of the expression

2L2mn – 3Lm2n + 4Lmn2 is Lmn.

Also, we can write 2L2mn = Lmn . 2L,   3Lm2n = Lmn . 3m  and  4Lmn2 = Lmn . 4n

Therefore, 2L2mn – 3Lm2n + 4Lmn2 =  (Lmn . 2L) –  (Lmn . 3m) +  (Lmn . 4n)

=  Lmn(2L – 3m + 4n)

Q.12)  x4y2 –  x2y4  – x4y4

Soln.:

The greatest common factor of the terms x4y2, x2y4  and x4y4 of the expressinon

x4y2 –  x2y4  – x4y4 is x2y2

Also, we can write  x4y2  =  (x2y2 . x2) ,  x2y4 = (x2y2 . y2)  and  x4y4 =  (x2y2 . x2y2)

Therefore,  x4y2 –  x2y4  – x4y4 = (x2y2 . x2) –  (x2y2 . y2) –  (x2y2 . x2y2)

= x2y2 (x2 – y2 – x2y2)

Q.13)  9x2y + 3axy

Soln.:

The greatest common factor of the terms 9x2y and 3axy of the expression 9x2y + 3axy is 3xy.

Also, we can write  9x2y = 3xy . 3x  and 3axy = 3xy . a

Therefore, 9x2y + 3axy = (3xy . 3x) + (3xy . a)

= 3xy (3x + a)

Q.14)  16m – 4m2

Soln.:

The greatest common factor of the terms 16m and 4m2 of the expression 16m – 4m2 is 4m.

Also, we can write 16m = 4m . 4  and 4m2 = 4m . m

Therefore, 16m – 4m2 = (4m . 4) – (4m . m)

= 4m(4 – m)

Q.15)  -4a2 + 4ab – 4ca

Soln.:

The greatest common factor of the terms -4a2 , 4ab and -4ca of the expression

-4a2 + 4ab – 4ca is -4a.

Also, we can write  -4a2 = (-4a . a) , 4ab = -4a . (-b) ,and  4ca = (-4a . c)

Therefore, -4a2 + 4ab – 4ca = (-4a . a) + (-4a . (-b)) – (4a . c)

=  -4a (a – b + c)

Q.16)  x2yz + xy2z + xyz2  

Soln.:

The greatest common factor of the terms x2yz , xy2z  and xyz2 of the expression

x2yz + xy2z + xyz2   is xyz.

Also, we can write x2yz  = (xyz . x)  , (xy2z = xyz . y) , xyz2 = (xyz . z)

Therefore, x2yz + xy2z + xyz2  = (xyz . x) + ( xyz . y) + (xyz . z)

= xyz(x + y + z)

 

Q.17)  ax2y + bxy2 + cxyz

Soln.:

The greatest common factor of the terms ax2y , bxy2 and cxyz  of the expression

ax2y + bxy2 + cxyz is xy.

Also, we can write ax2y = (xy . ax) , bxy2 = (xy . by) , cxyz = (xy . cz)

Therefore, ax2y + bxy2 + cxyz = (xy . ax) + (xy . by) + (xy . cz)

= xy (ax + by + cz)


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