Question

One factor of (x – y)³ – (x³ – y³) is ______.

विकल्प

• 3xy

• x²y²

• x + y

• x³y³

Answer 1

One factor of (x – y)³ – (x³ – y³) is 3xy.

Explanation:

The expression is (x – y)³ – (x³ – y³).

Recall the factorization formulas:

• a³ – b³ = (a – b)(a² + ab + b²).

Rewrite the second part:

x³ – y³ = (x – y)(x² + xy + y²).

So, (x – y)³ – (x³ – y³) = (x – y)³ – (x – y)(x² + xy + y²).

Take out the common factor (x – y): 

(x – y) [(x – y)² – (x² + xy + y²)]

Expand (x – y)² = x² – 2xy + y², so inside the bracket: 

(x² – 2xy + y²) – (x² + xy + y²) = –3xy

Thus, the whole expression factors as:

(x – y)(–3xy) = –3xy(x – y)

Hence, one factor is 3xy.