Question

Expand the following
- expand (4-1/3x)^3

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

[4 - (1/3x)]³

To find,

Expand: [4 - (1/3x)]³

Solution,

After expanding the given expression, we will get 64 - 1/27x³ + 4/3x² - 16/x.

We can easily solve this problem by following the given process.

We know that the identity (a-b)³ is a³ - b³ -3ab (a-b).

Now, the given expression fits in the identity [4 - (1/3x)]³.

Using the identity (a-b)³,

[4 - (1/3x)]³ = (4)³ - (1/3x)³ - 4/x [4 - (1/3x)]

[4 - (1/3x)]³ = 64 - 1/27x³ - 16/x + 4/3x²

[4 - (1/3x)]³ = 64 - 1/27x³ + 4/3x² - 16/x.

Hence, after expanding the given expression, we get 64 - 1/27x³ + 4/3x² - 16/x.

[More identities to know: (a+b)² = a² + b² + 2ab, (a-b)² = a² + b² - 2ab, and (a+b)³ = a³ + b³ + 3ab(a+b).]

( These identities are to be learnt to solve the problems based on them.)