Which of the following is a factor of (x + y)3 – (x3 + y3 )? (A) x2

1.	Which of the following is a factor of (x + y)3 – (x3 + y3 )? (A) x2 + y2 + 2xy (B) x2 + y2 – xy (C) xy2(D) 3xy
Answer» (d) 3xy Now, (x+ y)³ – (x³ + y³) = (x + y) – (x + y)(x²– xy + y²) [using identity, a³ + b³ = (a + b)(a² -ab+ b²)] = (x+ y)[(x+ y)² -(x² -xy+ y²)] = (x+ y)(x²+ y²+ 2xy- x²+ xy- y²) [using identity, (a + b)² = a² + b² + 2 ab)] = (x + y) (3xy) Hence, one of the factor of given polynomial is 3xy.

Which of the following is a factor of (x + y)3 – (x3 + y3 )? (A) x2 + y2 + 2xy (B) x2 + y2 – xy (C) xy2(D) 3xy

Answer»

(d) 3xy

Now, (x+ y)³ – (x³ + y³)

= (x + y) – (x + y)(x²– xy + y²)
[using identity, a³ + b³ = (a + b)(a² -ab+ b²)] = (x+ y)[(x+ y)² -(x² -xy+ y²)]

= (x+ y)(x²+ y²+ 2xy- x²+ xy- y²)
[using identity, (a + b)² = a² + b² + 2 ab)]

= (x + y) (3xy)

Hence, one of the factor of given polynomial is 3xy.