# 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

**☛ Related Questions:**

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