Expand the following : (1/x + y/3)³
Solution:
Given, (1/x + y/3)³
We have to expand (1/x + y/3)³
Using algebraic identity,
(a + b)³ = a³ + b³ + 3a(b)(a + b)
Here a = 1/x and b = y/3
So, (1/x + y/3)³ = (1/x)³ + (y/3)³ + 3(1/x)(y/3)(1/x + y/3)
= 1/x³ + y³/27 + y/x(1/x + y/3)
= 1/x³ + y³/27 + y/x² + y²/3x
Therefore, (1/x + y/3)³ = 1/x³ + y/x² + y²/3x + y³/27
✦ Try This: Expand the following : (3/x - 1/y)³
Given, (3/x - 1/y)³
We have to expand (3/x - 1/y)³
Using algebraic identity,
(a - b)³ = a³ - b³ + 3a(-b)(a - b)
Here a = 3/x and b = 1/y
So, (3/x - 1/y)³ = (3/x)³ - (1/y)³ + 3(3/x)(1/y)(3/x - 1/y)
= 27/x³ - 1/y³ - 9/xy(3/x - 1/y)
= 27/x³ - 1/y³ - 27/x²y + 9/xy²
Therefore, (3/x - 1/y)³ = 27/x³ - 27/x²y + 9/xy² - 1/y³
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 31(ii)
Expand the following : (1/x + y/3)³
Summary:
On expanding (1/x - y/3)³ using the algebraic identity we get 1/x³ - y/x² + y²/3x - y³/27
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