RD Sharma 2020 solution class 9 chapter 5 Factorization of Algebraic Expressions Exercise 5.3

Exercise 5.3

Page-5.17

Question 1:

Factorize:

64a³ + 125b³ + 240a²b + 300ab²
 

Answer 1:

The given expression to be factorized is

This can be written in the form

Take common from the last two terms,

This can be written in the following form

Recall the formula for the cube of the sum of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization of is.

Question 2:

125x³ − 27y³ − 225x²y + 135xy²

Answer 2:

The given expression to be factorized is

This can be written in the form

Take common from the last two terms,. Then we get

This can be written in the following form

Recall the formula for the cube of the difference of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is of is.

Question 3:

$\frac{8}{27}{x}^3+1+\frac{4}{3}{x}^2+2x$

Answer 3:

The given expression to be factorized is

This can be written in the form

Take common from the last two terms,. Then we get

This can be written in the following form

Recall the formula for the cube of the sum of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is of is.

Question 4:

8x³ + 27y³ + 36x²y + 54xy²

Answer 4:

The given expression to be factorized is

This can be written in the form

Take common from the last two terms. Then we get

This can be written in the following form

Recall the formula for the cube of the sum of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is of is.

Question 5:

a³ − 3a²b + 3ab² − b³ + 8

Answer 5:

The given expression to be factorized is

This can be written in the form

Take common from the third and fourth terms. Then we get

This can be written in the following form

Recall the formula for the cube of the difference of two numbers

Using the above formula, we have

This can be written in the following form

Recall the formula for the sum of two cubes

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is ofis.

Question 6:

x³ + 8y³ + 6x²y + 12xy²

Answer 6:

The given expression to be factorized is

This can be written in the form

Take common from the last two terms. Then we get

This can be written in the following form

Recall the formula for the cube of the sum of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is of is.

Page-5.18

Question 7:

8x³ + y³ + 12x²y + 6xy²

Answer 7:

The given expression to be factorized is

This can be written in the form

Take common 6xy from the last two terms,. Then we get

This can be written in the following form

Recall the formula for the cube of the sum of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is of is.

Question 8:

8a³ + 27b³ + 36a²b + 54ab²

Answer 8:

The given expression to be factorized is

This can be written in the form

Take common from the last two terms,. Then we get

This can be written in the following form

Recall the formula for the cube of the sum of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is of is.

Question 9:

8a³ − 27b³ − 36a²b + 54ab²

Answer 9:

The given expression to be factorized is

This can be written in the form

Take common – 18ab from the last two terms,. Then we get

This can be written in the following form

Recall the formula for the cube of the difference of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is ofis.

Question 10:

x³ − 12x(x − 4) − 64

Answer 10:

The given expression to be factorized is

This can be written in the form

Take common – 12x from the last two terms,. Then we get

This can be written in the following form

Recall the formula for the cube of the difference of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is of is.

Question 11:

a³x³ − 3a²bx² + 3ab²x − b³

Answer 11:

The given expression to be factorized is

This can be written in the form

Take common from the last two terms,. Then we get

This can be written in the following form

Recall the formula for the cube of the difference of two numbers

Using the above formula, we have

We cannot further factorize the expression. 

So, the required factorization is of is.