### Page No. 4.11

### Exercise : 4.2

**Question No. 1**

In the given problem, we have to find expended form

(i) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(ii) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(iii) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is.

(iv) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(v) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is.

(vi) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is.

(vii) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form ofis .

(viii) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(ix) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(x) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(xi) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(xii) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is.

### Page No. 4.11

### Exercise : 4.2

**Question No. 2**

In the given problem, we have to simplify the expressions

(i) Given

By using identity

Hence the equation becomes

Taking 2 as common factor we get

Hence the simplified value of is

(ii) Given

By using identity

Hence the equation becomes

Taking 4 as common factor we get

Hence the simplified value of is.

(iii) Given

By using identity , we have

Taking 3 as a common factor we get

Hence the value ofis

.

(iv) Given

By using identity , we get

By canceling the opposite terms, we get

Taking as common a factor we get,

Hence the value of is

(v) We have

Using formula, we get

By canceling the opposite terms, we get

Taking as common factor we get

Hence the value of is.

### Page No. 4.12

### Exercise : 4.2

**Question No. 3**

In the given problem, we have to find value of

Given and

Squaring the equation, we get

Now putting the value of in above equation we get,

Taking 2 as common factor we get

Hence the value of is .

### Page No. 4.12

### Exercise : 4.2

**Question No. 4**

In the given problem, we have to find value of

Given

Multiply equation with 2 on both sides we get,

Now adding both equation and we get

We shall use the identity

Hence the value of is .

### Page No. 4.12

### Exercise : 4.2

**Question No. 5**

In the given problem, we have to find value of

Given

Squaring both sides of we get,

Substituting in above equation we get,

Hence the value of is.

### Page No. 4.12

### Exercise : 4.2

**Question No. 6**

In the given problem, we have to find value of

Given

We have

This equation can also be written as

Using the identity

Hence the value of is .

### Page No. 4.12

### Exercise : 4.2

**Question No. 7**

In the given problem, we have to simplify the value of each expression

(i) Given

We shall use the identity for each bracket

By arranging the like terms we get

Now adding or subtracting like terms,

Hence the value of is

(ii) Given

We shall use the identity for expanding the brackets

Now arranging liked terms we get,

Hence the value of is

(iii) Given

We shall use the identity for each brackets

Canceling the opposite term and simplifies

Hence the value of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 1**

In the given problem, we have to find cube of the binomial expressions

(i) Given

We shall use the identity

Here

By applying the identity we get

Hence cube of the binomial expression is

(ii) Given

We shall use the identity

Here

By applying the identity we get

Hence cube of the binomial expression of is

(iii) Given

We shall use the identity

Here,

By applying identity we get

Hence cube of the binomial expression of is

(iv) Given

We shall use the identity

Here

By applying in identity we get

Hence cube of the binomial expression of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 2**

In the given problem, we have to simplify equation

(i) Given

We shall use the identity

Here

By applying identity we get

Hence simplified form of expression is .

(ii) Given

We shall use the identity

Here

By applying identity we get

By rearranging the variable we get

Hence the simplified value of is

(iii) Given

We shall use the identity

Here

By applying identity we get

By rearranging the variable we get,

Hence the simplified value of is

(iv) Given

We shall use the identity

Here

By applying the identity we get

By rearranging the variable we get,

Hence the simplified value of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 3**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

Hence the value of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 4**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

Hence the value of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 5**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

Hence the value of is

### Page No. 4.19

### Exercise : 4.3

**Question No. 6**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

Hence the value of is

### Page No. 4.19

### Exercise : 4.3

**Question No. 7**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

Hence the value of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 8**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

In order to find we are using identity

Here and

Hence the value of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 9**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

In order to find we are using identity

Here and

Hence the value of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 10**

In the given problem, we have to find the value of

Given,

In order to find we are using identity

Here putting,

Hence the value of is .

### Page No. 4.19

### Exercise : 4.3

**Question No. 11**

In the given problem, we have to find the value of

Given,

In order to find we are using identity

Here putting,,

Hence the value of is.

### Page No. 4.20

### Exercise : 4.3

**Question No. 12**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

In order to find we are using identity

In order to find we are using identity

Here and

Hence the value of is .

### Page No. 4.20

### Exercise : 4.3

**Question No. 13**

In the given problem, we have to find the value of numbers

(i) Given

In order to find we are using identity

We can write as

Hence where

The value of is

(ii) Given

In order to find we are using identity

We can write as

Hence where

The value of is

(iii) Given

In order to find we are using identity

We can write as

Hence where

The value of is

(iv) Given

In order to find we are using identity

We can write as

Hence where

The value of is

(v) Given

In order to find we are using identity

We can write as

Hence where

The value of is

(vi) Given

In order to find we are using identity

We can write as

Hence where

The value of is .

### Page No. 4.20

### Exercise : 4.3

**Question No. 14**

In the given problem, we have to find the value of numbers

(i) Given

We can write as

We shall use the identity

Here

Hence the value of is

(ii) Given

We can write as

We shall use the identity

Here

Hence the value of is

(iii) Given

We can write as

We shall use the identity

Here

Hence the value of is

(iv) Given

We can write as

We shall use the identity

Here

Hence the value of is .

### Page No. 4.20

### Exercise : 4.3

**Question No. 15**

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

Again squaring on both sides we get,

We shall use the identity

Again cubing on both sides we get,

We shall use identity

Hence the value of is respectively.

### Page No. 4.20

### Exercise : 4.3

**Question No. 16**

In the given problem, we have to find the value of

Given

By adding and subtracting in left hand side of we get,

Again by adding and subtracting in left hand side of we get,

Now cubing on both sides of we get

we shall use identity

Hence the value of is respectively.

### Page No. 4.20

### Exercise : 4.3

**Question No. 17**

In the given problem, we have to find the value of

(i) Given

On cubing both sides we get,

We shall use identity

Hence the value of is

(ii) Given

On cubing both sides we get,

We shall use identity

Hence the value of is .

### Page No. 4.20

### Exercise : 4.3

**Question No. 18**

From given problem we have to find the value of

Given

On cubing both sides of we get

We shall use identity

Hence the value of is .

### Page No. 4.20

### Exercise : 4.3

**Question No. 19**

In the given problem, we have to find the value of

Given

Cubing on both sides of we get

We shall use identity

Hence the value of is .

### Page No. 4.23

### Exercise : 4.4

**Question No. 1**

In the given problem, we have to find the value of

(i) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(ii) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(iii) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(iv) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(v) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(vi) Given

We shall use the identity ,

we can rearrange the as

Hence the Product value of is

(vii) Given

We shall use the identity,

We can rearrange the as

Hence the Product value of is

(viii) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(ix) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(x) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(xi) Given

We shall use the identity

We can rearrange the as

Hence the Product value of is

(xii) Given

We shall use the identity,

We can rearrange the as

Hence the Product value of is .

### Page No. 4.24

### Exercise : 4.4

**Question No. 2**

In the given problem, we have to find the value of equation using identity

(i) Given

We shall use the identity

We can rearrange the as

Now substituting the value in we get,

Hence the Product value of is

(ii) Given

We shall use the identity

We can rearrange the as

Now substituting the value x = 3, in we get,

Hence the Product value of is

(iii) Given

We shall use the identity,

We can rearrange the as

Now substituting the value in

Taking Least common multiple, we get

Hence the Product value of is

(iv) Given

We shall use the identity

We can rearrange the as

Now substituting the value in we get,

Taking Least common multiple, we get

Hence the Product value of is

(v) Given

We shall use the identity,

We can rearrange the as

Now substituting the value in

Taking Least common multiple, we get

Hence the Product value of is .

### Page No. 4.24

### Exercise : 4.4

**Question No. 3**

In the given problem, we have to find the value of

Given

We shall use the identity

We can rearrange the identity as

Now substituting values in as,

We can write as

Now rearrange as

Thus

Now substituting values

Hence the value of is respectively.

### Page No. 4.24

### Exercise : 4.4

**Question No. 4**

In the given problem, we have to find the value of

Given

We shall use the identity

Hence the value of is .

### Page No. 4.24

### Exercise : 4.4

**Question No. 5**

In the given problem, we have to find the value of

Given

We shall use the identity

Hence the value of is .

### Page No. 4.24

### Exercise : 4.4

**Question No. 6**

(i) In the given problem, we have to find the value of using identity

Given

We shall use the identity

We can rearrange the as

Now substituting the value in we get,

Taking 64 as common factor in above equation we get,

Hence the Product value of is

(ii) In the given problem, we have to find the value of using identity

Given

We shall use the identity

We can rearrange the as

Now substituting the value in we get,

Hence the Product value of is = 0.

(iii) Given

We shall use the identity,

We can rearrange the as

Now substituting the value in

Hence the Product value of is

### Page No. 4.28

### Exercise : 4.5

**Question No. 1**

In the given problem, we have to find Product of equations

(i)Given

We shall use the identity

Hence the product of is

(ii) Given

We shall use the identity

Hence the product of is

(iii) Given

We shall use the identity

Hence the product of is

(iv) Given

We shall use the identity

Hence the product of is

### Page No. 4.28

### Exercise : 4.5

**Question No. 2**

In the given problem, we have to find value of

Given

We shall use the identity

We know that

Here substituting we get

Hence the value of is .

### Page No. 4.28

### Exercise : 4.5

**Question No. 3**

In the given problem, we have to find value of

Given

We shall use the identity

We know that

Here substituting we get,

Hence the value of is .

### Page No. 4.28

### Exercise : 4.5

**Question No. 4**

In the given problem, we have to find value of

Given

We shall use the identity

We know that

Here substituting we get

Hence the value of is .

### Page No. 4.28

### Exercise : 4.5

**Question No. 5**

In the given problem we have to evaluate the following

(i) Given

We shall use the identity

Let Take

Hence the value of is

(ii) Given

We shall use the identity

Let Take

Hence the value of is

(iii) Given

We shall use the identity

Let Take

Applying least common multiple we get,

Hence the value of is

(iv) Given

We shall use the identity

Let Take

Hence the value of is

### Page No. 4.28

### Formative Assessment_VSA

**Question No. 1**

We have to find the value of

Given

Using identity

Here

By substituting the value of we get,

By transposing + 2 to left hand side, we get

Hence the value of is .

### Page No. 4.28

### Formative Assessment_VSA

**Question No. 2**

We have to find the value of

Given

Using identity

Here

By substituting the value of We get,

By transposing + 2 to left hand side, we get

Cubing on both sides we get,

Using identity

Here

Put we get

By transposing + 21 to left hand side we get ,

Hence the value of is .

### Page No. 4.28

### Formative Assessment_VSA

**Question No. 3**

We have to find the value of

Given

Using identity

By substituting the value of we get

By transposing +24 to left hand side we get ,

Hence the value of is .

### Page No. 4.29

### Formative Assessment_VSA

**Question No. 4**

We have to find the value

Given

Using identity

By substituting the value of we get ,

By transposing – 24 to left hand side we get

Hence the value of is .

### Page No. 4.29

### Formative Assessment_VSA

**Question No. 5**

We have to find the value of

Given

Using identity

Here

By substituting the value of we get

By transposing – 2 to left hand side we get

By taking least common multiply we get

By multiplying 4 on both sides we get

Hence the value of is

### Page No. 4.29

### Formative Assessment_VSA

**Question No. 6**

We have to find the value of

Given

Using identity

Here

By substituting we get

Hence the value of is

### Page No. 4.29

### Formative Assessment_VSA

**Question No. 7**

We have to find the value of

Given

Using identity

Put

Hence the value of is

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