Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma Solutions: Factorization of Algebraic Expressions- 2
Factorization of Algebraic Expressions- 2 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download
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Page 1
Question:36
Factorize each of the following expressions:
p
3
+ 27
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:37
y
3
+ 125
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
Page 2
Question:36
Factorize each of the following expressions:
p
3
+ 27
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:37
y
3
+ 125
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:38
1 - 27a
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:39
8x
3
y
3
+ 27a
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:40
64a
3
- b
3
Solution:
The given expression to be factorized is
This can be written in the form
Page 3
Question:36
Factorize each of the following expressions:
p
3
+ 27
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:37
y
3
+ 125
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:38
1 - 27a
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:39
8x
3
y
3
+ 27a
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:40
64a
3
- b
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:41
x
3
216
-8y
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:42
10x
4
y - 10xy
4
Solution:
The given expression to be factorized is
Take common from the two terms,. Then we have
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
Page 4
Question:36
Factorize each of the following expressions:
p
3
+ 27
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:37
y
3
+ 125
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:38
1 - 27a
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:39
8x
3
y
3
+ 27a
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:40
64a
3
- b
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:41
x
3
216
-8y
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:42
10x
4
y - 10xy
4
Solution:
The given expression to be factorized is
Take common from the two terms,. Then we have
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:43
54x
6
y + 2x
3
y
4
Solution:
The given expression to be factorized is
Take common from the two terms,. Then we have
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:44
32a
3
+ 108b
3
Solution:
The given expression to be factorized is
Take common from the two terms,. Then we have
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
Page 5
Question:36
Factorize each of the following expressions:
p
3
+ 27
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:37
y
3
+ 125
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:38
1 - 27a
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:39
8x
3
y
3
+ 27a
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:40
64a
3
- b
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:41
x
3
216
-8y
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:42
10x
4
y - 10xy
4
Solution:
The given expression to be factorized is
Take common from the two terms,. Then we have
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:43
54x
6
y + 2x
3
y
4
Solution:
The given expression to be factorized is
Take common from the two terms,. Then we have
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:44
32a
3
+ 108b
3
Solution:
The given expression to be factorized is
Take common from the two terms,. Then we have
This can be written in the form
Recall the formula for sum of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:45
(a - 2b)
3
- 512b
3
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:46
8x
2
y
3
- x
5
Solution:
The given expression to be factorized is
Take common . Then we have
This can be written as
Recall the formula for difference of two cubes
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization of is .
Question:47
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FAQs on Factorization of Algebraic Expressions- 2 RD Sharma Solutions - Mathematics (Maths) Class 9
| 1. What is factorization of algebraic expressions? |  |
Ans. Factorization of algebraic expressions is the process of breaking down an algebraic expression into its simplest form by finding its factors. The factors are obtained by dividing the expression by its common factors or using specific factorization techniques.
| 2. How is factorization useful in algebraic expressions? | |
Ans. Factorization is useful in algebraic expressions as it helps in simplifying the expressions and solving equations. It allows us to identify common factors, which can be canceled out to simplify complex expressions. Factorization also helps in solving quadratic equations and finding the roots of a polynomial equation.
| 3. What are the common factorization techniques used in algebraic expressions? | |
Ans. The common factorization techniques used in algebraic expressions include:
1. Factoring out the greatest common factor (GCF): This involves identifying and factoring out the largest common factor from all the terms of the expression.
2. Difference of squares: This technique is used to factorize expressions of the form a^2 - b^2, where a and b are real numbers.
3. Perfect square trinomials: This technique is used to factorize expressions of the form a^2 + 2ab + b^2 or a^2 - 2ab + b^2, where a and b are real numbers.
4. Grouping: This technique involves grouping the terms of the expression in a specific way to factorize it.
| 4. How can factorization help in solving equations? | |
Ans. Factorization can help in solving equations by simplifying the expressions involved. When an equation is factorized, it can be rewritten in terms of its factors, which makes it easier to find the values of the variables that satisfy the equation. By equating each factor to zero, we can determine the possible solutions of the equation.
| 5. Can all algebraic expressions be factorized? | |
Ans. No, not all algebraic expressions can be factorized. Some expressions are prime or irreducible, meaning that they cannot be factored into simpler expressions. However, most polynomial expressions can be factorized using the techniques mentioned earlier. It is important to note that factorization is not always straightforward and may require complex algebraic manipulations in some cases.
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Nov 22, 2024 Last updated |
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