Mister Exam

# How do you ((3x+3y)^3−(3x+y)^3)/(27x^2+36xy+13y^2) in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
           3            3
(3*x + 3*y)  - (3*x + y)
-------------------------
2                2
27*x  + 36*x*y + 13*y  
$$\frac{- \left(3 x + y\right)^{3} + \left(3 x + 3 y\right)^{3}}{13 y^{2} + \left(27 x^{2} + 36 x y\right)}$$
((3*x + 3*y)^3 - (3*x + y)^3)/(27*x^2 + (36*x)*y + 13*y^2)
Fraction decomposition [src]
2*y
$$2 y$$
2*y
General simplification [src]
2*y
$$2 y$$
2*y
(27.0*(x + y)^3 - 27.0*(x + 0.333333333333333*y)^3)/(13.0*y^2 + 27.0*x^2 + 36.0*x*y)
(27.0*(x + y)^3 - 27.0*(x + 0.333333333333333*y)^3)/(13.0*y^2 + 27.0*x^2 + 36.0*x*y)
Combinatorics [src]
2*y
$$2 y$$
2*y
Assemble expression [src]
           3            3
(3*x + 3*y)  - (y + 3*x)
-------------------------
2       2
13*y  + 27*x  + 36*x*y 
$$\frac{- \left(3 x + y\right)^{3} + \left(3 x + 3 y\right)^{3}}{27 x^{2} + 36 x y + 13 y^{2}}$$
((3*x + 3*y)^3 - (y + 3*x)^3)/(13*y^2 + 27*x^2 + 36*x*y)
Trigonometric part [src]
           3            3
(3*x + 3*y)  - (y + 3*x)
-------------------------
2       2
13*y  + 27*x  + 36*x*y 
$$\frac{- \left(3 x + y\right)^{3} + \left(3 x + 3 y\right)^{3}}{27 x^{2} + 36 x y + 13 y^{2}}$$
((3*x + 3*y)^3 - (y + 3*x)^3)/(13*y^2 + 27*x^2 + 36*x*y)
Powers [src]
           3            3
(3*x + 3*y)  - (y + 3*x)
-------------------------
2       2
13*y  + 27*x  + 36*x*y 
$$\frac{- \left(3 x + y\right)^{3} + \left(3 x + 3 y\right)^{3}}{27 x^{2} + 36 x y + 13 y^{2}}$$
((3*x + 3*y)^3 - (y + 3*x)^3)/(13*y^2 + 27*x^2 + 36*x*y)
Rational denominator [src]
           3            3
(3*x + 3*y)  - (y + 3*x)
-------------------------
2       2
13*y  + 27*x  + 36*x*y 
$$\frac{- \left(3 x + y\right)^{3} + \left(3 x + 3 y\right)^{3}}{27 x^{2} + 36 x y + 13 y^{2}}$$
((3*x + 3*y)^3 - (y + 3*x)^3)/(13*y^2 + 27*x^2 + 36*x*y)
Combining rational expressions [src]
           3             3
- (y + 3*x)  + 27*(x + y)
--------------------------
2
13*y  + 9*x*(3*x + 4*y)  
$$\frac{27 \left(x + y\right)^{3} - \left(3 x + y\right)^{3}}{9 x \left(3 x + 4 y\right) + 13 y^{2}}$$
(-(y + 3*x)^3 + 27*(x + y)^3)/(13*y^2 + 9*x*(3*x + 4*y))
Common denominator [src]
2*y
$$2 y$$
2*y