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

VSAQS

Page-5.27

Question 1:

If a + b + c = 0, then write the value of a³ + b³ + c³.

Answer 1:

Recall the formula

When, we have

Question 2:

If a² + b² + c² = 20 and a + b + c = 0, find ab + bc + ca.

Answer 2:

Recall the formula

Given that

Then we have

Question 3:

If a + b + c = 9 and ab + bc + ca = 40, find a² + b² +c².

Answer 3:

Recall the formula

Given that
,
Then we have

Question 4:

If a² + b² + c² = 250 and ab + bc + ca = 3, find a + b + c.

Answer 4:

Recall the formula

Given that
,
Then we have

Question 5:

Write the value of 25³ − 75³ + 50³.

Answer 5:

The given expression is

Let, and. Then the given expression becomes

Note that

Recall the formula

When, this becomes

So, we have the new formula
, when.
Using the above formula, the value of the given expression is

Question 6:

Write the value of 48³ − 30³ − 18³.

Answer 6:

The given expression is

Let, and. Then the given expression becomes

Note that

Recall the formula

When, this becomes 

So, we have the new formula
, when.
Using the above formula, the value of the given expression is

Page-5.28

Question 7:

Write the value of ${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^3.$

Answer 7:

The given expression is

Let, and. Then the given expression becomes

Note that:

Recall the formula

When, this becomes

So, we have the new formula
, when.
Using the above formula, the value of the given expression is

Question 8:

Write the value of 30³ + 20³ − 50³.

Answer 8:

The given expression is

Let, and. Then the given expression becomes

Note that

Recall the formula

When, this becomes


So, we have the new formula
, when.
Using the above formula, the value of the given expression is

Question 9:

Factorize: x⁴ + x² + 25.

Answer 9:

The given expression to be factorized is
This can be written in the form

We cannot further factorize the expression. 
So, the required factorization is.

Question 10:

Factorize : x² − 1 − 2a − a²

Answer 10:

The given expression to be factorized is

Take commonfrom the last three terms and then we have 


We cannot further factorize the expression. 
So, the required factorization is.

Page-5.28

Question 7:

Write the value of ${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^3.$

Answer 7:

The given expression is

Let, and. Then the given expression becomes

Note that:

Recall the formula

When, this becomes

So, we have the new formula
, when.
Using the above formula, the value of the given expression is

Question 8:

Write the value of 30³ + 20³ − 50³.

Answer 8:

The given expression is

Let, and. Then the given expression becomes

Note that

Recall the formula

When, this becomes


So, we have the new formula
, when.
Using the above formula, the value of the given expression is

Question 9:

Factorize: x⁴ + x² + 25.

Answer 9:

The given expression to be factorized is
This can be written in the form

We cannot further factorize the expression. 
So, the required factorization is.

Question 10:

Factorize : x² − 1 − 2a − a²

Answer 10:

The given expression to be factorized is

Take commonfrom the last three terms and then we have 


We cannot further factorize the expression. 
So, the required factorization is.