Simplify the following expression: (x−3y)
3
+27(y
3
−xy
2
)

Expand the first term using the identity (a−b)
3
=a
3
−3a
2
b+3ab
2
−b
3
:

(x−3y)
3
=x
3
−3(x
2
)(3y)+3(x)(3y)
2
−(3y)
3

(x−3y)
3
=x
3
−9x
2
y+27xy
2
−27y
3

Now expand the second term:

27(y
3
−xy
2
)=27y
3
−27xy
2

Add the two parts together:

Expression=(x
3
−9x
2
y+27xy
2
−27y
3
)+(27y
3
−27xy
2
)
Combine the like terms:

The +27xy
2
and −27xy
2
cancel each other out.

The −27y
3
and +27y
3
cancel each other out.

Thus, the simplified expression is:

x
3
−9x
2
y