Question

Question 17
Which of the following is a factor of $(x+y{)}^3–(x^3+y^3)$?

A) $x^2+y^2+2xy$
B) $x^2+y^2–xy$
C) $x{y}^2$
​​​​​​​D) $3xy$

Answer 1

The answer is D.
Now, $(x+y{)}^3-(x^3+y^3)=(x+y{)}^3–(x+y)(x^2-xy+y^2)$
[Using identity, $a^3+b^3=(a+b)(a^2-ab+b^2)$]
$=(x+y)\left[\right(x+y{)}^2–(x^2–xy+y^2)]$
$=(x+y)(x^2+y^2+2xy-x^2+xy-y^2)$
[Using identity, $(a+b{)}^2=a^2+b^2+2ab)$]
$=(x+y)\left(3xy\right)$
Hence, one of the factor of given polynomial is 3xy.