Factorization in Mathematics is the breaking down of a Mathematical object into a product of other factors, which, when multiplied together, gives the original. Here, students will learn how to factorize algebraic equations through solved RD Sharma Solutions Class 9. The solutions are written in simple language to grasp the concepts easily. The RD Sharma Solutions can be downloaded from the link given below.
RD Sharma Solutions for Class 9 Maths Chapter 5 Factorization of Algebraic Expressions Exercise VSAQs
Access Answers to Maths RD Sharma Solutions for Class 9 Chapter 5 Factorization of Algebraic Expressions Exercise VSAQs Page Number 5.24
Exercise VSAQs Page No: 5.24
Question 1: Factorize x4 + x2 + 25
Solution:
x4 + x2 + 25
= (x2) 2 + 52 + x2
[using a2 + b2 = (a + b) 2 – 2ab ]= (x2 +5) 2 −2(x2 ) (5) + x2
= (x2 +5) 2 −10x2 + x2
= (x2 + 5) 2 − 9x2
= (x2 + 5) 2 − (3x) 2
[using a2 – b2 = (a + b)(a – b ]= (x 2 + 3x + 5)(x2 − 3x + 5)
Question 2: Factorize x2 – 1 – 2a – a2
Solution:
x2 – 1 – 2a – a2
x2 – (1 + 2a + a2 )
x2 – (a + 1)2
(x – (a + 1)(x + (a + 1)
(x – a – 1)(x + a + 1)
[using a2 – b2 = (a + b)(a – b) and (a + b)^2 = a^2 + b^2 + 2ab ]Question 3: If a + b + c =0, then write the value of a3 + b3 + c3.
Solution:
We know, a3 + b3 + c3 – 3abc = (a + b +c ) (a2 + b2 + c2 – ab – bc − ca)
Put a + b + c =0
This implies
a3 + b3 + c3 = 3abc
Question 4: If a2 + b2 + c2 = 20 and a + b + c =0, find ab + bc + ca.
Solution:
We know, (a+b+c)² = a² + b² + c² + 2(ab + bc + ca)
0 = 20 + 2(ab + bc + ca)
-10 = ab + bc + ca
Or ab + bc + ca = -10
Question 5: If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 + c2 .
Solution:
We know, (a+b+c)² = a² + b² + c² + 2(ab + bc + ca)
92 = a² + b² + c² + 2(40)
81 = a² + b² + c² + 80
⇒ a² + b² + c² = 1
RD Sharma Solutions for Class 9 Maths Chapter 5 Factorization of Algebraic Expressions Exercise VSAQs
RD Sharma Solutions for Class 9 Maths Chapter 5 Factorization of Algebraic Expressions Exercise VSAQs are based on the following topics:
- Factorization by grouping the terms
- Factorization by making a perfect square
- Factorization by the difference of two squares
- Factorization of algebraic expressions expressible as the sum or difference of two cubes
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