Factorise the following : 1 - 64a³ - 12a + 48a²

Solution:

Given, the expression is 1 - 64a³ - 12a + 48a² -------- (1)

We have to factorise the expression.

Using the algebraic identity,

Using algebraic identity,

(a - b)³ = a³ - b³ - 3a²b + 3ab² ------------- (2)

On comparing (1) and (2),

a³ = 1

a = 1

b³ = 64a³

b = 4a

-3a²b = 12a

a²b = -4a

(1)²b = -4a

So, b = -4a

3ab² = 48a²

ab² = 16a²

b² = 4a

Here a = 1 and b = -4a

So, (a - b)³ = (1 - 4a)³ 

Therefore, the factors of the given expression are (1 - 4a), (1 - 4a) and (1 - 4a).

✦ Try This: Factorise the following : 1 - 8a³ - 6a + 12a²

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

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NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 32(i)

Factorise the following : 1 - 64a³ - 12a + 48a²

Summary:

On factorising 1 - 64a³ - 12a + 48a² we get the factors as (1 - 4a), (1 - 4a) and (1 - 4a)

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