Question

Question 59 (a)

What should be added to $x^3+3x^{2}y+3x{y}^2+y^3$ to get $x^3+y^3?$

Answer 1

In order to find the solution subtract $x^3+3x^{2}y+3x{y}^2+y^3$ from $x^3+y^3.$
Required expression is
$x^3+y^3-(x^3+3x^{2}y+3x{y}^2+y^3)=x^3+y^3-x^3-3x^{2}y-3x{y}^2-y^3$
On combining the like terms.
$=x^3-x^3+y^3-y^3-3x^{2}y-3x{y}^2=-3x^{2}y-3x{y}^2$
So, if we add $-3x^{2}y-3x{y}^2$ in $x^3+3x^{2}y+3x{y}^2+y^3$, we get $x^3+y^3.$