Question

17. Which of the following is a factor of (x+y)^3 - (x^3 + y^3)?
(a) x² + y^2 +2 xy
(b) x² + y2 - xy
(c) xy^2
(d) 3xy​

Answer 1

Answer:

(d) 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.

Answer 2

Question :- To find factor of (x + y)³ - (x³ + y³) ?

Sᴏʟᴜᴛɪᴏɴ :-

→ (x + y)³ - (x³ + y³)

using (a³ + b³) = (a + b)(a² + b² - ab) we get,

→ (x + y)³ - (x+y)(x² + y² - xy)

Taking (x + y) common Now, we get,

→ (x + y)[(x + y)² - (x² + y² - xy)]

Now, Using (a+b)² = a² + b² + 2ab we get,

→ (x + y)[(x² + y² + 2xy) - (x² + y² - xy)]

→ (x + y)[x² + y² + 2xy - x² - y² + xy)]

→ (x + y)[ 2xy + xy ]

→ (x + y) * (3xy)

Hence, we can conclude That, 3xy(D) Option is a Factor of given Polynomial.