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1.(v) Find the remainder whenx^ 3 + 3x^ 2 + 3x + 1 is divided by
   (v)   5+2x

16.(ii)  What are the possible expressions for the dimensions of the cuboid whose volumes is given below?

                    (ii)

    Volume :    12ky^2 + 8ky - 20k
We know that  Volume of cuboid is =   It is given that volume  =   Now,                                                                                                                                                                                                  Therefore,one of the possible answer is possible  Length =   and  Breadth =   and  Height =    

16.(i)    What are the possible expressions for the dimensions of the cuboid whose volumes is given below?

                    (i)

    Volume :    3x^2 - 12x

 

We know that  Volume of cuboid is =   It is given that volume  =   Now,  Therefore,one of the possible answer is possible  Length =   and  Breadth =   and  Height =    

15.(ii)  Give possible expressions for the length and breadth of the following rectangle, in which its area is given:

                    (ii)    

    Area:    35y^2 + 13y- 12
We know that  Area of rectangle is =   It is given that area  =   Now, by splitting the middle term method                                                                                       Therefore, two answers are possible  case (i) :-   Length =   and  Breadth =  case (ii) :-   Length =   and  Breadth = 

15.(i)  Give possible expressions for the length and breadth of the following rectangle, in which its area is given:

                    (i)    

    Aera:    25a^2 - 35a + 12

 

We know that  Area of rectangle is =   It is given that area  =   Now, by splitting middle term method                                                                                       Therefore, two answers are possible  case (i) :-   Length =   and  Breadth =  case (ii) :-   Length =   and  Breadth = 

14.(ii) Without actually calculating the cubes, find the value of the following:
      (ii)   (28)^3 + (-15)^3 + (-13)^3

Given is    We know that    If      then ,    Here,  Therefore, Therefore, value of    is  

14.(i)  Without actually calculating the cubes, find the value of each of the following:
      (i)  (-12)^3 + (7)^3 + (5)^3

Given is    We know that    If      then ,    Here,  Therefore, Therefore, value of    is  

13. If x + y + z = 0, show that x^3 + y^3 + z^3 = 3xyz.

We know that Now, It is given that   Therefore, Hence proved 

12. Verify that    x^3 + y^3 + z^3 -3xyz = \frac{1}{2} ( x + y + z)\left[(x-y)^2 + (y-z)^2 + (z-x)^2 \right ]

We know that Now, multiply and divide the R.H.S. by 2                                                                                                                                   Hence proved 

11. Factorise:     27x^3 + y^3 + z^3 - 9xyz

Given is   Now, we know that  Now, we can write    as    Here,  Therefore,                                                    

10.(ii) Factorise the following:

      (ii)    64m^3 - 343n^3

We know that  Now, we can write    as  Here,   Therefore,

10.(i) Factorise the following:

      (i)    27y^3 + 125z^3

We know that  Now, we can write    as  Here,   Therefore,

9.(ii)  Verify:

    (ii)    x^3 - y^3 = (x -y)(x^2 + xy + y^2)

We know that Now,                                                                                             Hence proved 

9.(i) Verify:

   (i)    x^3 + y^3 = (x +y)(x^2 - xy + y^2)

We know that Now,                                                                                             Hence proved 

8.(v) Factorise the following:

    (v)    27p^3 - \frac{1}{216} - \frac{9}{2}p^2 + \frac{1}{4} p

We can rewrite     as   We will use identity Here,   Therefore,                                                     

8.(iv)  Factorise the following:

   (iv)    64a^3 - 27b^3 - 144a^2 b + 108ab^2

We can rewrite     as   We will use identity Here,   Therefore,                                                                    

8.(iii) Factorise the following:

    (iii)   27 - 125a^ 3 - 135a + 225a^2

We can rewrite     as   We will use identity Here,   Therefore,                                                            

8.(ii)  Factorise the following:

   (ii)    8a ^3 - b^3 - 12a^2 b + 6ab^2

We can rewrite     as   We will use identity Here,   Therefore,                                                     

8.(i) Factorise the following:

   (i) 8a^3 + b^3 + 12a^2 b + 6ab^2

We can rewrite     as   We will use identity Here,   Therefore,                                                     

7.(iii)  Evaluate the following using suitable identities:

    (iii)    (998)^3

We can rewrite     as We will use identity Here,   Therefore,                          
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