Question

Expand : (3x − 2y)³

Answer 1

To expand (3x − 2y)³, we use the binomial expansion formula:

(x−y)³ = x³ − 3x²y + 3xy² − y³

Here, x = 3x and y = 2y.

Apply the formula

(3x − 2y)³ = (3x)³ − 3(3x) 2(2y) + 3(3x)(2y)² − (2y)³

Simplify each term

1. (3x)³ = 27x³
2. −3(3x)²(2y) = −3(9x²)(2y) = −54x²y
3. 3(3x)(2y)² = 3(3x)(4y²) = 36xy²
4. −(2y)³ = −8y³

Combine the terms

(3x−2y)³ = 27x³ − 54x²y + 36xy² − 8y³

27x³ − 54x²y + 36xy² − 8y³