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1.(v) Find the remainder when is divided by
(v)

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

(ii)

 Volume :
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 :

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:
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:

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)

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)

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

13. If , show that .

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

12. Verify that

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

11. Factorise:

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

10.(ii) Factorise the following:

(ii)

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

10.(i) Factorise the following:

(i)

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

9.(ii)  Verify:

(ii)

We know that Now,                                                                                             Hence proved

9.(i) Verify:

(i)

We know that Now,                                                                                             Hence proved

8.(v) Factorise the following:

(v)

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

8.(iv)  Factorise the following:

(iv)

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

8.(iii) Factorise the following:

(iii)

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

8.(ii)  Factorise the following:

(ii)

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

8.(i) Factorise the following:

(i)

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

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

(iii)

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