- Home
- Std 9
- Mathematics
2. Polynomials
easy
Which of the following is a factor of $(x+y)^{3}-\left(x^{3}+y^{3}\right) ?$
A
$x^{2}+y^{2}+2 x y$
B
$3 x y$
C
$x^{2}+y^{2}-x y$
D
$x y^{2}$
Solution
$(x+y)^{3}-\left(x^{3}+y^{3}\right)=x^{3}+y^{3}+3 x y(x+y)-x^{3}-y^{3}$
$=3 x y(x+y)$
So, $3 x y$ is a factor of $(x+y)^{3}-\left(x^{3}+y^{3}\right)$.
Hence, $(b)$ is the correct answer.
Std 9
Mathematics
