Expand the following : (3a - 2b)³
Solution:
Given, (3a - 2b)³
We have to expand (3a - 2b)³
Using algebraic identity,
(a - b)³ = a³ - b³ + 3a(-b)(a - b)
Here a = 3a and b = 2b
So, (3a - 2b)³ = (3a)³ - (2b)³ + 3(3a)(-2b)(3a - 2b)
= 27a³ - 8b³ - 18ab(3a - 2b)
= 27a³ - 8b³ - 54a²b + 36ab²
Therefore, (3a - 2b)³ = 27a³ - 54a²b + 36ab² - 8b³
✦ Try This: Expand the following : (a - 2b)³
Given, (2a - 2b)³
We have to expand (2a - 2b)³
Using algebraic identity,
(a - b)³ = a³ - b³ + 3a(-b)(a - b)
Here a = 2a and b = 2b
So, (2a - 2b)³ = (2a)³ - (2b)³ + 3(2a)(-2b)(2a - 2b)
= 8a³ - 8b³ - 12ab(2a - 2b)
= 8a³ - 8b³ - 24a²b + 24ab²
Therefore, (2a - 2b)³ = 8a³ - 24a²b + 24ab² - 8b³
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 31(i)
Expand the following : (3a - 2b)³
Summary:
On expanding (3a - 2b)³ using the algebraic identity we get 27a³ - 54a²b + 36ab² - 8b³
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