Question

What will be the value of (2x - 3y)³ + 18xy(2x - 3y) ?
1. 8x³ + 27y³
2. 8x³ - 27y³
3. 8x³ + 27y³ - 18x²y
4. 8x³ + 27y³ - 18xy²

Answer 1

Correct Answer - Option 2 : 8x³ - 27y³

Given:

(2x - 3y)3 + 18xy(2x - 3y)

Formula used:

(a - b)³ = a³ - b³ - 3ab(a - b)

Calculation:

(2x - 3y)3 + 18xy(2x - 3y)

⇒ 8x³ - 27y³ - 3 × 2x × 3y(2x - 3y) + 18xy(2x - 3y)

⇒ 8x3 - 27y³ - 18xy(2x - 3y) + 18xy(2x - 3y)

⇒ 8x3 - 27y³ - 36x²y + 54xy² + 36x² - 54xy³

⇒ 8x3 - 27y³

∴ (2x - 3y)3 + 18xy(2x - 3y) = 8x3 - 27y3