Question

expand ; (3a-2b)^3 ​

Answer 1

Answer:

(3a-2b)³=27a³-8b³-54a²b+36ab²

Step-by-step explanation:

⇒(3a-2b)³=(3a)³-(2b)³-3(3a)(2b)[(3a)-(2b)]

⇒(3a-2b)³=27a³-8b³-18ab(3a-2b)

⇒(3a-2b)³=27a³-8b³-54a²b+36ab²

Since (a-b)³=a³+b³-3ab(a-b)

Answer 2

Given : The algebraic expression is, (3a-2b)³

To find : The expansion of the given algebraic expression.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to expand the given algebraic expression)

Here, we will be using necessary algebraic identities, in order to expand the given algebraic expression.

Now, we know that :

(x-y)³ = x³ - 3x²y + 3xy² - b³

In case of, (3a-4b)³

• x = 3a
• y = 4b

So, the expansion (according the previously mentioned algebraic identity) will be :

= (3a-4b)³

= (3a)³ - [3 × (3a)² × 4b] + [3 × 3a × (4b)²] - (4b)²

= 27a³-108a²b+144ab²-64b³

(This will be considered as the final result of the given mathematical problem.)

Hence, the answer to the expansion is, 27a³-108a²b+144ab²-64b³