Expand the following : (4 - 1/3x)³
Solution:
Given, (4 - 1/3x)³
We have to expand (4 - 1/3x)³
Using algebraic identity,
(a - b)³ = a³ - b³ + 3a(-b)(a - b)
Here a = 4 and b = 1/3x
So, (4 - 1/3x)³ = (4)³ - (1/3x)³ + 3(4)(-1/3x)(4 - 1/3x)
= 64 - 1/27x³ - 4/x(4 - 1/3x)
= 64 - 1/27x³ - 16/x + 4/3x²
Therefore, (4 - 1/3x)³ = 64 - 16/x + 4/3x² - 1/27x³
✦ Try This: Expand the following : (5 - 1/3y)³
Given, (5 - 1/3y)³
We have to expand (5 - 1/3y)³
Using algebraic identity,
(a - b)³ = a³ - b³ + 3a(-b)(a - b)
Here a = 5 and b = 1/3y
So, (5 - 1/3y)³ = (5)³ - (1/3y)³ + 3(5)(-1/3y)(5 - 1/3y)
= 125 - 1/27y³ - 5/y(5 - 1/3y)
= 125 - 1/27y³ - 25/y + 5/3y²
Therefore, (5 - 1/3y)³ = 125 - 25/y + 5/3y² - 1/27y³
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 31(iii)
Expand the following : (4 - 1/3x)³
Summary:
On expanding (4 - 1/3x)³ using the algebraic identity we get 64 - 16/x + 4/3x² - 1/27x³
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